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MEDICAL    .SCMOOL 
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CONTRIBUTIONS  TO  THE  ANALYSIS 
OF  THE  SENSATIONS. 


BY  THE  SAME  AUTHOR. 


The  Science  of  Mechanics.  A  Historical  and  Crit- 
ical Exposition  of  its  Principles.  Translated  from 
the  Second  German  Edition  by  T.  J.  McCormack. 
250  Cuts.  534  Pages.  Half  Morocco,  Gilt  Top. 
Price,  $2.50. 

Popular  Scientific  Lectures.  Translated  by  T. 
J.  McCormack.  313  Pages.  44  Cuts.  Cloth, 
$1.00  ;  Paper,  35  cents. 

Contributions  to  the  Analysis  of  the  Sensations. 
With  new  additions  by  the  author.  Translated 
by  C.  M.  Williams.  Pages,  208.  37  Cuts.  Price, 
$1.25,  net. 

THE   OPEN   COURT  PUBLISHING   CO., 

324  DEARBORN   ST.,  CHICAGO. 


CONTRIBUTIONS 


ANALYSIS  OF  THE  SENSATIONS 


RNST   MACH 


FORMERLY  PMF^SC*  OF  PHYSICS  IN  THE  UNIVERSITY  OF  PRAGUE,  NOW 

PROF^(Soi^(Mf  THE  HISTORY  AND  THEORY  OF  INDUCTIVE 

SCIENCE  IN  THE  UNIVERSITY  OF  VIENNA 


TRANSLATED 

BY 

C.  M.  WILLIAMS 


WITH  THIRTY-SEVEN  CUTS 


i»    €         »c 


-T     >  3  J  3 


CHICAGO 

THE    OPEN    COURT    PUBLISHING    COMPANY 

(LONDON  :   17  JOHNSON'S  COURT,  FLEET  ST.,  E.  C.) 

1897 


K 


Translation  and  original  matter  copyrighted,  1890,  1892,  and  1897  by 
The  Open  Court  Publishing  Co. 


•  •       •     • 

>•  •       •    • 

•  •       •   • 


PREFACE  TO  THE  ENGLISH  EDITION. 


FOR  the  preparation  of  the  present  excellent  translation  of 
my  Beitrdge  zur  Analyse  der  Empfindungen  I  am  under 
profound  obligations  to  The  Open  Court  Publishing  Company 
Not  a  little  of  the  progress  of  psychology  is  owing  to  the  strenuous 
efforts  which  the  promoters  of  the  science  have  made  to  find  the 
main  explanation  of  its  problems  in  the  principle  of  association 
and  these  investigations  have  received  a  fresh  impulse  from  the 
results  of  neural  anatomy  and  neural  physiology.  I  am  of  opinion 
however,  that  the  idea  advanced  in  the  present  work,  agreeably  to 
which  as  many  physico-chemical  neural  processes  are  to  be  as- 
sumed as  there  are  distinguishable  qualities  of  sensation,  is  also 
possessed  of  heuristic  value,  and  that  there  is  reasonable  hope  that 
at  some  future  time  it,  too,  will  receive  elucidation  from  the  side 
of  physiological  chemistry.  Admittedly,  this  idea,  which  is  but  a 
consistent,  monistic  conception  of  Miiller's  principle  of  the  specific 
energies,  is  not  in  accord  with  prevailing  notions.  By  the  example 
and  influence  of  a  great  authority  it  has  become  the  custum  to  rel- 
egate the  explanation  of  different  qualities  of  sensation  to  unknown 
domains,  and  to  regard  all  neural  processes  as  absolutely  alike 
qualitatively  and  only  quantitatively  different.  I  had  occasion  as 
early  as  1863  (Vor lesungen  iiber  Psychophysik,  Vienna,  Sommer, 
p.  33)  to  point  out  how  little  such  a  conception  is  calculated  to  lead 
to  a  profounder  knowledge  of  our  sensations,  and  how  little  justifi- 
able it  is,  even  from  a  physical  point  of  view,  to  regard  all  electric 


1^63 


vi  THE  ANALYSIS  OF  THE  SENSATIONS. 

neural  currents  as  physical  processes  qualitatively  the  same  in 
kind.  One  has  only  to  think  of  a  current  through  copper,  through 
sulphate  of  copper,  or  through  acidulated  water.  A  few  inquirers 
only,  like  Hering,  still  uphold  MUller's  doctrine  in  its  original  sig- 
nification, and  under  these  circumstances  the  opportunity  of  pre- 
senting my  thoughts  to  a  new  public  is  doubly  valuable. 

E.  Mach. 
Vienna,  September,  1896. 


ORIGINAL  PREFACE. 


THE  frequent  excursions  which  I  have  made  into  this  province 
have  all  sprung  from  the  profound  conviction  that  the  foun- 
dations of  science  as  a  whole,  and  of  physics  in  particular,  await 
their  next  greatest  elucidations  from  the  side  of  biology,  and  espe- 
cially from  the  analysis  of  the  sensations. 

I  am  aware,  of  course,  that  I  can  contribute  but  little  to  the 
attainment  of  this  end.  The  very  fact  that  my  investigations  have 
been  carried  on,  not  in  the  way  of  a  profession,  but  only  at  odd 
moments,  and  frequently  only  after  long  interruptions,  must  de- 
tract considerably  from  the  value  of  my  scattered  publications,  or 
perhaps  even  lay  me  open  to  the  secret  charge  of  desultoriness 
So  much  the  more,  therefore,  am  I  under  especial  obligations  to 
those  investigators,  such  as  E.  Hering,  V,  Hensen,  W.  Preyer 
and  others,  who  have  directed  attention  either  to  the  matter  of  my 
writings  or  to  their  methodological  outcome. 

The  present  compendious  and  supplementary  presentation  of 
my  views,  perhaps,  will  place  my  attitude  in  a  somewhat  more 
favorable  light,  for  it  will  be  seen  that  in  all  cases  I  have  had  in 
mind  the  same  problem,  no  matter  how  varied  or  numerous  were 
the  single  facts  investigated.  Although  I  can  lay  no  claim  what- 
ever to  the  title  of  physiologist,  and  still  less  to  that  of  philosopher, 
yet  I  venture  to  hope  that  the  work  thus  undertaken,  purely  from 
a  strong  desire  for  self-enlightenment,  by  a  physicist  unconstrained 
by  the  conventional  barriers  of  the  specialist,  may  not  be  entirely 


viii  THE  ANALYSIS  OF  THE  SENSATIONS. 

without  value  for  others  also,  even  though  I  may  not  be  every- 
where in  the  right. 

My  natural  bent  for  the  study  of  these  questions  received  its 
strongest  stimulus  from  Fechner's  Elemente  der  Psychophysik 
(Leipsic,  i860),  but  my  greatest  assistance  was  derived  from 
Hering's  solution  of  the  two  problems  referred  to  in  the  footnote 
of  page  35  and  in  the  text  of  page  81. 

To  readers  who,  for  any  reason,  desire  to  avoid  more  general 
discussions,  I  recommend  the  omission  of  the  first  and  last  chap- 
ters. For  me,  however,  the  conception  of  the  whole  and  the  con- 
ception of  the  parts  are  so  intimately  related  that  I  should  scarcely 
be  able  to  separate  them. 

The  Author. 

Prague,  November,  1885. 


TRANSLATOR'S  NOTE. 


THE  MATTER  contained  in  a  book  is  by  no  means  propor- 
tioned to  its  size.  If  this  were  so,  the  following  treatise, 
rich  as  it  is  in  suggestions  bearing  on  some  of  the  fundamental 
problems  of  scientific  and  philosophical  theory,  must  be  a  bulky 
one.  The  author  has  not,  however,  entered  into  any  detailed  ap- 
plication of  the  conclusions  drawn  from  his  observations  and  expe- 
riments, but  has  contented  himself  with  a  succinct  exposition  of 
those  conclusions,  leaving  to  the  reader  the  very  pleasurable  task 
of  following  out  the  many  trains  of  thought  opened  up  by  them 
The  German  edition  of  the  book  has  been  the  subject  of  great  in- 
terest and  discussion.  To  the  English  text  the  author  has  added 
considerable  new  matter  in  the  notes  on  pages  4,  20,  21,  26,  39, 
40,  56,  78,  82-83,  115.  and  in  the  two  Appendices. 

The  manuscript  and  proofs  of  this  edition  have  had  the  advan- 
tage of  revisal  by  Mr.  T.  J.  McCormack,  of  La  Salle,  Illinois 
translator  of  the  author's  Science  of  Mechanics,  who  also  inde- 
pendently rendered  the  "  Introductory  Remarks"  and  Appendix  I. 
— matter  which  originally  appeared  in  The  Monist. 

C.  M.  Williams. 

Boston,  December,  1896. 


CONTENTS. 


PAGE 


Introductory  Remarks.     Antimetaphysical i 

The  Chief  Points  of  View  for  the  Investigation  of  the  Senses.  27 

The  Space-Sensations  of  the  Eye 41 

Investigation  of  Space-Sensation  Continued 57 

The  Sight-Sensations. — Their  Relations  to  One  Another  and 

to  Other  Psychical  Elements 82 

Time-Sensation 109 

Sensations  of  Tone 119 

Physics. — Influence  of  the  Preceding   Investigations  on  the 

Mode  of  its  Conception 151 

Appendix  I. — Facts  and  Mental  Symbols 185 

Appendix  II. — "A  New  Acoustic  Experiment  by  E.  Mach"     .  197 

Addenda 200 


INTRODUCTORY  REMARKS. 


ANTIMETAPHYSICAL. 
I. 

THE  splendid  success  achieved  by  physical  science 
in  modern  times,  a  success  which  is  not  restricted 
to  its  own  sphere  but  embraces  that  of  other  sciences 
which  employ  its  help,  has  brought  it  about  that  phys- 
ical ways  of  thinking  and  physical  modes  of  procedure 
enjoy  on  all  hands  unwonted  prominence,  and  that  the 
greatest  expectations  are  associated  with  their  employ- 
ment. In  keeping  with  this  drift  of  modern  inquiry, 
the  physiology  of  the  senses,  gradually  leaving  the 
paths  which  were  opened  by  men  like  Goethe,  Scho- 
penhauer, and  others,  but  with  particular  success  by 
Johannes  Miiller,  has  also  assumed  an  almost  exclu- 
sively physical  character.  This  tendency  must  appear 
to  us  as  not  exactly  the  proper  one,  when  we  reflect  that 
physics  despite  its  considerable  development  never- 
theless constitutes  but  a  portion  of  a  larger  collective 
body  of  knowledge,  and  that  it  is  unable,  with  its  lim- 
ited intellectual  implements,  created  for  limited  and 
special  purposes,  to  exhaust   all   the  subject-matter 


2  THE  ANALYSIS  OF  THE  SENSATIONS. 

of  science.  Without  renouncing  the  support  of  phys- 
ics, it  is  possible  for  the  physiology  of  the  senses,  not 
only  to  pursue  its  own  course  of  development,  but  also 
to  afford  to  physical  science  itself  powerful  assistance  ; 
a  point  which  the  following  simple  considerations  will 
serve  to  illustrate. 


Colors,  sounds,  temperatures,  pressures,  spaces, 
times,  and  so  forth,  are  connected  with  one  another  in 
manifold  ways ;  and  with  them  are  associated  moods  of 
mind,  feelings,  and  volitions.  Out  of  this  fabric,  that 
which  is  relatively  more  fixed  and  permanent  stands 
prominently  forth,  engraves  itself  in  the  memory,  and 
expresses  itself  in  language.  Relatively  greater  per- 
manency exhibit,  first,  certain  complexes  of  colors, 
sounds,  pressures,  and  so  forth,  connected  in  time  and 
space,  which  therefore  receive  special  names,  and  are 
designated  bodies.  Absolutely  permanent  such  com- 
plexes are  not. 

My  table  is  now  brightly,  now  dimly  lighted.  Its 
temperature  varies.  It  may  receive  an  ink  stain.  One 
of  its  legs  may  be  broken.  It  may  be  repaired,  polished, 
and  replaced  part  for  part.  But  for  me,  amid  all  its 
changes,  it  remains  the  table  at  which  I  daily  write. 

My  friend  may  put  on  a  different  coat.  His  counte- 
nance may  assume  a  serious  or  a  cheerful  expression. 
His  complexion,  under  the  effects  of  light  or  emotion, 
may  change.     His  shape  may  be  altered  by  motion, 


INTRODUCTORY  REMARKS.  3 

or  be  definitely  changed.  Yet  the  number  of  the  per- 
manent features  presented,  compared  with  the  number 
of  the  gradual  alterations,  is  always  so  great,  that  the 
latter  may  be  overlooked.  It  is  the  same  friend  with 
whom  I  take  my  daily  walk. 

My  coat  may  receive  a  stain,  a  tear.  My  very  man- 
ner of  expression  shows  that  we  are  concerned  here 
with  a  sum-total  of  permanency,  to  which  the  new  ele- 
ment is  added  and  from  which  that  which  is  lacking  is 
subsequently  taken  away. 

Our  greater  intimacy  with  this  sum-total  of  per- 
manency, and  its  preponderance  as  contrasted  with 
the  changeable,  impel  us  to  the  partly  instinctive, 
partly  voluntary  and  conscious  economy  of  mental  rep- 
resentation and  designation,  as  expressed  in  ordinary 
thought  and  speech.  That  which  is  perceptually  repre- 
sented in  a  single  image  receives  a  single  designation, 
a  single  name. 

As  relatively  permanent,  is  exhibited,  further,  that 
complex  of  memories,  moods,  and  feelings,  joined  to 
a  particular  body  (the  human  body),  which  is  denom- 
inated the  '*I  "  or  *'Ego."  I  may  be  engaged  upon 
this  or  that  subject,  I  may  be  quiet  or  animated,  ex- 
cited or  ill-humored.  Yet,  pathological  cases  apart, 
enough  durable  features  remain  to  identify  the  ego. 
Of  course,  the  ego  also  is  only  of  relative  permanency.^ 

iThe  apparent  permanency  of  the  ego  consists  chiefly  in  the  fact  of  its 
continuity  and  in  the  slowness  of  its  changes.  The  many  thoughts  and  plans 
of  yesterday  that  are  continued  to-day,  and  of  which  our  environment  in  wak- 
ing hours  incessantly  reminds  us  (wherefore  in  dreams  the  ego  can  be  very  in- 


4  THE  ANALYSIS  OF  THE  SENSATIONS, 

After  a  first  survey  has  been  obtained,  by  the  form- 
ation of  the  substance-concepts  **body"  and  *'ego" 
(matter  and  soul),  the  will  is  impelled  to  a  more  exact 
examination  of  the  changes  that  take  place  in  these 
relatively  permanent  existences.  The  changeable  fea- 
tures of  bodies  and  of  the  ego,  in  fact,  are  exactly  what 
moves  the  will  to  this  examination.  Here  the  com- 
ponent parts  of  the  complex  are  first  exhibited  as  its 


distinct,  doubled,  or  entirely  wanting),  and  the  little  habits  that  are  uncon- 
sciously and  involuntarily  kept  up  for  long  periods  of  time,  constitute  the 
groundwork  of  the  ego.  There  can  hardly  be  greater  differences  in  the  egos 
of  different  people,  than  occur  in  the  course  of  years  in  one  person.  When  I 
recall  to-day  my  early  youth,  I  should  take  the  boy  that  I  then  was,  with  the 
exception  of  a  few  individual  features,  for  a  different  person,  did  not  the 
chain  of  memories  that  make  up  my  personality  lie  actually  before  me.  Many 
an  article  that  I  myself  penned  twenty  years  ago  impresses  me  now  as  some- 
thing quite  foreign  to  myself.  The  very  gradual  character  of  the  changes  of  the 
body  also  contributes  to  the  stability  of  the  ego,  but  in  a  much  less  degree  than 
people  imagine.  Such  things  are  much  less  analysed  and  noticed  than  the 
intellectual  and  the  moral  ego.  Personally,  people  know  themselves  very 
poorly. 

Once,  when  a  young  man,  I  espied  in  the  street  the  profile  of  a  face  that 
was  very  displeasing  and  repulsive  to  me.  I  was  not  a  little  taken  aback  when 
a  moment  afterwards  I  found  that  it  was  my  own,  which,  in  passing  by  a  place 
where  mirrors  were  sold,  I  had  perceived  reflected  from  two  mirrors  that 
were  inclined  at  the  proper  angle  to  each  other. 

Not  long  ago,  after  a  trying  railway  journey  by  night,  and  much  fatigued, 
I  got  into  an  omnibus,  just  as  another  gentleman  appeared  at  the  other  end. 
"What  degenerate  pedagogue  is  that,  that  has  just  entered,"  thought  I.  It 
was  myself:  opposite  me  hung  a  large  mirror.  The  physiognomy  of  my  class, 
accordingly,  was  better  known  to  me  than  my  own. 

The  ego  is  as  little  absolutely  permanent  as  are  bodies.  That  which  we 
so  much  dread  in  death,  the  annihilation  of  our  permanency,  actually  occurs 
in  life  in  abundant  measure.  That  which  is  most  valued  by  us,  remains  pre- 
served in  countless  copies,  or,  in  cases  of  exceptional  excellence,  is  even  pre- 
served of  itself.  In  the  best  human  being,  however,  there  are  individual 
traits,  the  loss  of  which  neither  he  himself  nor  others  need  regret.  Indeed, 
at  times,  death,  viewed  as  a  liberation  from  individuality,  may  even  become 
a  pleasant  thought.  [When  I  wrote  these  lines,  Ribot's  admirable  little  book, 
771^  Diseases  of  Personality,  second  edition,  Paris,  1888,  Chicago,  iggj,  was  un- 
known to  me.  Ribot  ascribes  the  principal  rOle  in  preserving  the  continuity 
of  the  ego  to  the  general  sensibility.  Generally,  I  am  in  perfect  accord  with 
his  views.— Mach,  1895.] 


INTR  OD  UCTOR  V  REMARKS.  5 

properties.  A  fruit  is  sweet;  but  it  can  also  be  bitter. 
Also,  other  fruits  may  be  sweet.  The  red  color  we  are 
seeking  is  found  in  many  bodies.  The  neighborhood 
of  some  bodies  is  pleasant ;  that  of  others,  unpleasant. 
Thus,  gradually,  different  complexes  are  found  to  be 
made  up  of  common  elements.  The  visible,  the  aud- 
ible, the  tangible,  are  separated  from  bodies.  The 
visible  is  analysed  into  colors  and  into  form.  In  the 
manifoldness  of  the  colors,  again,  though  here  fewer 
in  number,  other  component  parts  are  discerned — 
such  as  the  primary  colors,  and  so  forth.  The  com- 
plexes are  disintegrated  into  elements. 


The  useful  habit  of  designating  such  relatively  per- 
manent compounds  by  single  names,  and  of  apprehend- 
ing them  by  single  thoughts,  without  going  to  the 
trouble  each  time  of  an  analysis  of  their  component 
parts,  is  apt  to  come  into  strange  conflict  with  the 
tendency  to  isolate  the  component  parts.  The  vague 
image  which  we  have  of  a  given  permanent  complex, 
being  an  image  which  does  not  perceptibly  change 
when  one  or  another  of  the  component  parts  is  taken 
away,  gradually  establishes  itself  as  something  which 
exists  by  itself.  Inasmuch  as  it  is  possible  to  take 
away  singly  every  constituent  part  without  destroying 
the  capacity  of  the  image  to  stand  for  the  totality  and 
of  being  recognised  again,  it  is  imagined  that  it  is  pos- 


6  THE  ANALYSIS  OF  THE  SENSATIONS. 

sible  to  subtract  all  the  parts  and  to  have  something 
still  remaining.  Thus  arises  the  monstrous  notion  of 
a  thing  in  itself^  unknowable  and  different  from  its 
"phenomenal"  existence. 

Thing,  body,  matter,  are  nothing  apart  from  their 
complexes  of  colors,  sounds,  and  so  forth — nothing 
apart  from  their  so-called  attributes.  That  Protean, 
supposititious  problem,  which  springs  up  so  much  in 
philosophy,  of  a  single  thing  with  many  attributes, 
arises  wholly  from  a  mistaking  of  the  fact,  that  sum- 
mary comprehension  and  precise  analysis,  although 
both  are  provisionally  justifiable  and  for  many  pur- 
poses profitable,  cannot  and  must  not  be  carried  on 
simultaneously.  A  body  is  one  and  unchangeable  only 
so  long  as  it  is  unnecessary  to  consider  its  details. 
Thus  both  the  earth  and  a  billiard-ball  are  spheres,  if 
the  purpose  in  hand  permits  our  neglecting  deviations 
from  the  spherical  form,  and  great  precision  is  not 
necessary.  But  when  we  are  obliged  to  carry  on  in- 
vestigations in  orography  or  microscopy,  both  bodies 
cease  to  be  spheres. 


Man  possesses,  in  its  highest  form,  the  power  of 
consciously  and  arbitrarily  determining  his  point  of 
view.  He  can  at  one  time  disregard  the  most  salient 
features  of  an  object,  and  immediately  thereafter  give 
attention  to  its  smallest  details ;  now  consider  a  sta- 
tionary current,  without  a  thought  of  its  contents,  and 


INTR  OD  UCTOR  Y  REMARKS.  7 

then  measure  the  width  of  a  Fraunhofer  line  in  the 
spectrum ;  he  can  rise  at  will  to  the  most  general  ab- 
stractions or  bury  himself  in  the  minutest  particulars. 
The  animal  possesses  this  capacity  in  a  far  less  degree. 
It  does  not  assume  a  point  of  view,  but  is  usually 
forced  to  it.  The  babe  who  does  not  know  its  father 
with  his  hat  on,  the  dog  that  is  perplexed  at  the  new 
coat  of  its  master,  have  both  succumbed  in  this  conflict 
of  points  of  view.  Who  has  not  been  worsted  in  similar 
plights?  Even  the  man  of  philosophy  at  times  suc- 
cumbs, as  the  grotesque  problem,  above  referred  to, 
shows. 

In  this  last  case,  the  circumstances  appear  to  fur- 
nish a  real  ground  of  justification.  Colors,  sounds, 
and  the  odors  of  bodies  are  evanescent.  But  the  tan- 
gible part,  as  a  sort  of  constant,  durable  nucleus,  not 
readily  susceptible  of  annihilation,  remains  behind  ; 
appearing  as  the  vehicle  of  the  more  fugitive  proper- 
ties annexed  to  it.  Habit,  thus,  keeps  our  thought 
firmly  attached  to  this  central  nucleus,  even  where  the 
knowledge  exists  that  seeing,  hearing,  smelling,  and 
touching  are  intimately  akin  in  character.  A  further 
consideration  is,  that  owing  to  the  singularly  extensive 
development  of  mechanical  physics  a  kind  of  higher 
reality  is  ascribed  to  space  and  time  than  to  colors, 
sounds,  and  odors ;  agreeably  to  which,  the  temporal 
and  spatial  links  of  colors,  sounds,  and  odors  appear 
to  be  more  real  than  the  colors,  sounds,  and  odors 
themselves.     The  physiology  of  the  senses,  however, 


8  THE  ANALYSIS  OF  THE  SENSATIONS. 

demonstrates,  that  spaces  and  times  may  just  as  ap- 
propriately be  called  sensations  as  colors  and  sounds. 

5- 

The  ego,  and  the  relation  of  bodies  to  the  ego,  give 
rise  to  similar  pseudo-problems,  the  character  of  which 
may  be  briefly  indicated  as  follows  : 

Let  those  complexes  of  colors,  sounds,  and  so 
forth,  commonly  called  bodies,  be  designated,  for  the 
sake  of  simplicity,  hy  ABC .  .  .;  the  complex,  known 
as  our  own  body,  which  constitutes  a  part  of  the  former, 
may  be  called  KLM .  .  .;  the  complex  composed  of 
volitions,  memory-images,  and  the  rest,  we  shall  repre- 
sent \iy  apy .  .  .  Usually,  now,  the  complex  a/3y.  .  . 
KLM.  .  .,  as  making  up  the  ego,  is  opposed  to  the 
complex  ABC...,  as  making  up  the  world  of  sub- 
stance; sometimes,  also,  a^y .  .  .  is  viewed  as  ego, 
and  KLM.  .ABC.  .  .  as  world  of  substance.  Now, 
at  first  blush,  ABC.  .  .  appears  independent  of  the 
ego,  and  opposed  to  it  as  a  separate  existence.  But 
this  independence  is  only  relative,  and  gives  way  upon 
closer  inspection.  Much,  it  is  true,  may  change  in  the 
complex  afty.  .  .  without  a  perceptible  change  being 
induced  mABC...)  and  vice  versa.  But  many  changes 
in  a /3y .  .  .  do  pass,  by  way  of  changes  in  KLM.  .  ., 
to  ^  ^  C  .  . ;  and  vice  versa.  (As,  for  example,  when 
powerful  ideas  burst  forth  into  acts,  or  our  environ- 
ment induces  noticeable  changes  in  our  body.)  At  the 
same  time  the  group  ^Z  J/...   appears   to  be  more 


INTRODUCTORY  REMARKS.  9 

intimately  connected  with  a Py .  .  .  and  with  ABC.  .  . , 
than  the  latter  do  with  one  another ;  relations  which 
find  their  expression  in  common  thought  and  speech. 

Precisely  viewed,  however,  it  appears  that  the  group 
ABC...  is  always  codetermined  by  K L  M.  A  cube 
of  wood  when  seen  close  at  hand,  looks  large ;  when 
seen  at  a  distance,  small ;  it  looks  different  with  the 
right  eye  from  what  it  does  with  the  left ;  sometimes 
it  appears  double ;  with  closed  eyes  it  is  invisible. 
The  properties  of  the  same  body,  therefore,  appear 
modified  by  our  own  body;  they  appear  conditioned 
by  it.  But  where,  now,  is  that  same  body,  which  to 
the  appearance  is  so  different  ?  All  that  can  be  said 
is,  that  with  different  KLM  different  ABC...  are 
associated.^ 

We  see  an  object  having  a  point  S.  If  we  touch 
S,  that  is,  bring  it  into  connexion  with  our  body,  we 
receive  a  prick.  We  can  see  S,  without  feeling  the 
prick.  But  as  soon  as  we  feel  the  prick  we  find  S. 
The  visible  point,  therefore,  is  a  permanent  fact  or  nu- 


1 A  long  time  ago  (in  the  Vierteljahrssckri/t/ur  Psychiatrie,  Leipsic  and 
Neuwied,  1868,  art.  "  Ueber  die  Abhangigkeit  der  Netzhautstellen  von  einan- 
der,"  I  enunciated  this  thought  as  follows  :  The  expression  "  sense-illusion" 
proves  that  we  are  not  yet  fully  conscious,  or  at  least  have  not  yet  deemed  it 
necessary  to  incorporate  the  fact  into  our  ordinary  language,  that  the  senses 
represent  things  neither  wrongly  nor  correctly.  All  that  can  be  truly  said  of 
the  sense-organs  is,  that,  under  different  circumstances  they  produce  different 
sensations  and  perceptions.  As  these  "circumstances,"  now,  are  extremely 
manifold  in  character,  being  partly  external  (inherent  in  the  objects),  partly 
internal  (inherent  in  the  sensory  organs),  and  partly  interior  (having  their 
seat  in  the  central  organs),  it  would  naturally  seem,  especially  when  attention 
is  paid  only  to  external  circumstances,  as  if  the  organs  acted  differently  under 
the  same  conditions.  And  it  is  customary  to  call  the  unusual  effects,  decep- 
tions or  illusions. 


lo  THE  ANALYSIS  OF  THE  SENSATIONS. 

cleus,  to  which  the  prick  is  annexed,  according  to  cir- 
cumstances, as  something  accidental.  From  the  fre- 
quency of  such  occurrences  we  ultimately  accustom 
ourselves  to  regard  ail  properties  of  bodies  as  ''effects" 
proceeding  from  permanent  nuclei  and  conveyed  to 
the  ego  through  the  medium  of  the  body  ;  which  effects 
we  call  sensations.  By  this  operation,  however,  our 
imagined  nuclei  are  deprived  of  their  entire  sensory 
contents,  and  converted  into  mere  mental  symbols. 
The  assertion,  then,  is  correct  that  the  world  consists 
only  of  our  sensations.  In  which  case  we  have  knowl- 
edge oniy  of  sensations,  and  the  assumption  of  the  nu- 
clei referred  to,  or  of  a  reciprocal  action  between  them, 
from  which  sensations  proceed,  turns  out  to  be  quite 
idle  and  superfluous.  Such  a  view  can  only  suit  with 
a  half-hearted  realism  or  a  half-hearted  philosophical 
criticism. 


Ordinarily  the  complex  a  fty .  .  .  KLM .  .  .  is  con- 
trasted as  ego  with  the  complex  ABC.  Those  elements 
only  ol  A  B  C. . .  that  more  strongly  alter  a /3y. .  .,  as 
a  prick,  a  pain,  are  wont  to  be  comprised  in  the  ego. 
Afterwards,  however,  through  observations  of  the  kind 
just  referred  to,  it  appears  that  the  right  to  annex 
ABC...  to  the  ego  nowhere  ceases.  In  conformity 
with  this  view  the  ego  can  be  so  extended  as  ultimately 
to  embrace  the  entire  world. ^     The  ego  is  not  sharply 

IWhen  I  say  that  the  table,  the  tree,  and  so  forth,  are  my  sensations,  the 
statement,  as  contrasted  witli  the  mode  of  representation  of  the  ordinary  man, 


INTR  OD  UCTOR  Y  REMARKS.  t  r 

marked  off,  its  limits  are  very  indefinite  and  arbitrarily 
displaceable.  Only  by  failing  to  observe  this  fact,  and 
by  unconsciously  narrowing  those  limits,  while  at  the 
same  time  we  enlarge  them,  arise,  in  the  conflict  of 
points  of  view,  the  metaphysical  difficulties  met  with  in 
this  connexion. 

As  soon  as  we  have  perceived  that  the  supposed 
unities ''body '*  and  ''ego"  are  only  makeshifts,  de- 
signed for  provisional  survey  and  for  certain  practical 
ends  (so  that  we  may  take  hold  of  bodies,  protect  our- 
selves against  pain,  and  so  forth),  we  find  ourselves 
obliged,  in  many  profound  scientific  investigations,  to 
abandon  them  as  insufficient  and  inappropriate.  The 
antithesis  of  ego  and  world,  sensation  (phenomenon) 
and  thing,  then  vanishes,  and  we  have  simply  to  deal 
with  the  connexion  of  the  elements  afty...ABC... 
K LM .  .  .,  of  which  this  antithesis  was  only  a  partially 
appropriate  and  imperfect  expression.  This  connex- 
ion is  nothing  more  nor  less  than  the  combination  of 
the  above-mentioned  elements  with  other  similar  ele- 
ments (time  and  space).  Science  has  simply  to  accept 
this  connexion,  and  to  set  itself  aright  (get  its  bear- 
ings) in  the  intellectual  environment  which  is  thereby 
furnished,  without  attempting  to  explain  its  existence. 

involves  a  real  extension  of  my  ego.  On  the  emotional  side  also  such  exten- 
sions occur,  as  in  the  case  of  the  virtuoso,  who  possesses  as  perfect  a  mastery 
of  his  instrument  as  he  does  of  his  own  body;  or  in  the  case  of  the  skilful 
orator,  on  whom  the  eyes  of  the  audience  are  all  converged,  and  who  is  con- 
trolling the  thoughts  of  all ;  or  in  that  of  the  able  politician  who  is  deftly 
guiding  his  party;  and  so  on.  In  conditions  of  depression,  on  the  other  hand 
such  as  nervous  people  often  endure,  the  ego  contracts  and  shrinks.  A  wall 
seems  to  separate  it  from  the  world. 


12  THE  ANALYSIS  OF  THE  SENSATIONS. 

On  a  superficial  examination  the  complex  ocfty. . . 
appears  to  be  made  up  of  much  more  evanescent  ele- 
ments than  ABC...  and  K L  M .  .  .  in  which  last  the 
elements  seem  to  be  connected  with  greater  stability 
and  /;/  a  more  permanent  manner  (being  joined  to  solid 
nuclei  as  it  were).  Although  on  closer  inspection  the 
elements  of  all  complexes  prove  to  be  homogeneous^  yet 
in  spite  of  the  knowledge  of  this  fact,  the  early  notion 
of  an  antithesis  of  body  and  spirit  easily  regains  the 
ascendancy  in  the  mind.  The  philosophical  spiritualist 
is  often  sensible  of  the  difficulty  of  imparting  the  needed 
solidity  to  his  mind-created  world  of  bodies ;  the  ma- 
terialist is  at  a  loss  when  required  to  endow  the  world 
of  matter  with  sensation.  The  monistic  point  of  view, 
which  artificial  reflexion  has  evolved,  is  easily  clouded 
by  our  older  and  more  powerful  instinctive  notions. 

7- 

The  difficulty  referred  to  is  particularly  felt  in  the 
following  case.  In  the  complex  ABC.  .  .,  which  we 
have  called  the  world  of  matter,  we  find  as  parts,  not 
only  our  own  body  K LM .  .  .,  but  also  the  bodies  of 
other  persons  (or  animals)  K'L'M'.  .  .,  K"L"M".  .  ., 
to  which,  by  analogy,  we  imagine  other  a'ft'y' ,  .  ., 
a"  ^"  y".  .  .,  annexed,  similar  to  a  fty  ...  So  long  as 
we  deal  with  K'L'M'.  .  .,  we  find  ourselves  in  a  thor- 
oughly familiar  province  at  every  point  sensorially 
accessible  to  us.  When,  however,  we  inquire  after 
the  sensations  or  feelings  appurtenant   to  the  body 


INTRO D  UCrOR  V  REMARKS.  13 

K'L'M'.  .  .,  we  no  longer  find  the  elements  we  seek 
in  the  province  of  sense  :  we  add  them  in  thought.  Not 
only  is  the  domain  which  we  now  enter  far  less  familiar 
to  us,  but  the  transition  into  it  is  also  relatively  un- 
safe. We  have  the  feeling  as  if  we  were  plunging  into 
an  abyss. ^  Persons  who  adopt  this  method  only,  will 
never  thoroughly  rid  themselves  of  this  sense  of  inse- 
curity, which  is  a  frequent  source  of  illusive  problems. 
But  we  are  not  restricted  to  this  course.  Let  us 
consider,  first,  the  reciprocal  relations  of  the  elements 
of  the  complex^ -5  C  .  .,  without  regarding ^Z  J/.  .  . 
(our  body).  All  physical  investigations  are  of  this 
sort.  A  white  bullet  falls  upon  a  bell ;  a  sound  is 
heard.  The  bullet  turns  yellow  before  a  sodium  lamp, 
red  before  a  lithium  lamp.  Here  the  elements  {ABC. . .) 
appear  to  be  connected  only  with  one  another  and  to  be 
independent  of  our  body  {KLM.  .  .).  But  if  we  take 
santonine,  the  bullet  again  turns  yellow.  If  we  press 
one  eye  to  the  side,  we  see  two  bullets.  If  we  close 
our  eyes  entirely,  we  see  none  at  all.     If  we  sever  the 

IWhen  I  first  came  to  Vienna  from  the  country,  as  a  boy  of  four  or  five 
years,  and  was  taken  by  my  father  upon  the  walls  of  the  city's  fortifications, 
I  was  very  much  surprised  to  see  people  below  in  the  moat,  and  could  not 
understand  how,  from  my  point  of  view,  they  could  have  got  there;  for  the 
thought  of  another  way  of  descent  never  occurred  to  me.  I  remarked  the 
same  astonishment,  once  afterwards  in  life,  in  the  case  of  a  three-year-old 
boy  of  my  own,  while  walking  on  the  walls  of  Prague.  I  recall  this  feeling 
every  time  I  occupy  myself  with  the  reflexion  of  the  text,  and  I  frankly  con- 
fess that  this  accidental  experience  of  mine  helped  to  confirm  my  opinion 
upon  this  point,  which  I  have  now  long  held.  The  habit  of  pursuing  the  same 
methods  in  material  and  psychical  questions  tends  greatly  to  confuse  our  field 
of  survey.  A  child,  on  the  piercing  of  the  wall  of  a  house  in  which  it  has 
long  dwelt,  may  experience  a  veritable  enlargement  of  its  world-view,  and 
in  the  same  manner  a  slight  scientific  hint  may  often  attord  great  enlighten- 
ment. 


14  THE  ANALYSIS  OF  THE  SENSATIONS. 

auditory  nerve,  no  sound  is  heard.  The  elements 
ABC,  .  .,  therefore,  are  not  only  connected  among 
one  another,  but  also  with  KLM.  To  this  extent, 
and  to  this  extent  only,  do  we  call  ABC...  sensatiofis, 
and  regard  A  B  C  SiS  belonging  to  the  ego.  In  this  way, 
accordingly,  we  do  not  find  the  gap  between  bodies 
and  sensations  above  described,  between  what  is  with- 
out and  what  is  within,  between  the  material  world 
and  the  spiritual  world. ^  All  elements  ABC..., 
KLM .  .  .  constitute  a  single  coherent  mass  only,  in 
which,  when  any  one  element  is  disturbed,  all  is  put 
in  motion ;  except  that  a  disturbance  in  KLM.  .  .  has 
a  more  extensive  and  profound  action  than  in  ABC. 
A  magnet  in  our  neighborhood  disturbs  the  particles 
of  iron  near  it ;  a  falling  boulder  shakes  the  earth ; 
but  the  severing  of  a  nerve  sets  in  motion  the  whole 
system  of  elements.* 

8. 
That  traditional  gulf  between  physical  and  psycho- 
logical research,  accordingly,  exists  only  for  the  habit- 
ual stereotyped  method  of  observation.  A  color  is  a 
physical  object  so  long  as  we  consider  its  dependence 
upon  its  luminous  source,  upon  other  colors,  upon 
heat,  upon  space,  and  so  forth.  Regarding,  however,  its 
dependence  upon  the  retina  (the  elements  KLM .  .  .), 

1  Compare  my  Grundlinien  der  Lehre  von  den  Bewegungsempfindungeji 
Leipsic  :  Engelmann,  1875,  p.  54. 

2  Quite  involuntarily  does  this  relation  of  things  suggest  the  picture  of  a 
viscous  mass,  at  certain  places  (as  in  the  ego)  more  firmly  coherent  than  in 
others.    I  have  often  made  use  of  this  simile  in  lectures. 


INTR  OD  UC  TOR  Y  RE  MA  RKS.  15 

it  becomes  a  psychological  object,  a  sensation.  Not 
the  subject,  but  the  direction  of  our  investigation,  is 
different  in  the  two  domains. 

Both  in  reasoning  from  the  observation  of  the 
bodies  of  other  men  or  animals,  to  the  sensations  which 
they  possess,  as  well  as  in  investigating  the  influence 
of  our  own  body  upon  our  own  sensations,  we  must 
complete  observed  facts  by  analogy.  This  is  accom- 
plished with  much  greater  readiness  and  certainty, 
when  it  relates,  say,  only  to  nervous  processes,  which 
cannot  be  fully  observed  in  our  own  bodies — that  is, 
when  it  is  carried  out  in  the  more  familiar  physical 
domain — than  when  it  is  made  in  connexion  with  psy- 
chical processes.  Otherwise  there  is  no  essential  dif- 
ference. 


The  considerations  advanced  will  gain  in  strength 
and  vividness  by  a  concrete  example.  Thus,  I  lie 
upon  my  sofa.  If  I  close  my  right  eye,  the  picture 
represented  in  the  accompanying  cut  is  presented  to 
my  left  eye.  In  a  frame  formed  by  the  ridge  of  my 
eyebrow,  by  my  nose,  and  by  my  moustache,  appears 
a  part  of  my  body,  so  far  as  visible,  with  its  environ- 
ment.^ My  body  differs  from  other  human  bodies — 
beyond  the  fact  that  every  intense  motor  idea  is  imme- 
diately expressed  by  a  movement  of  it,  and  that  its 

lA  discussion  of  the  binocular  field  of  vision,  with  its  peculiar  stereo- 
scopic features,  is  omitted  here,  for  although  familiar  to  all,  it  is  not  as  easy 
to  describe,  and  cannot  be  represented  by  a  single  plane  drawing. 


i6  THE  ANALYSIS  OF  THE  SENSATIONS. 

being  touched  determines  more  striking  changes  than 
contact  with  other  bodies — by  the  circumstance,  that 
it  is  only  partly  seen,  and,  especially,  is  seen  without 


Fig. 


a  head.  If  I  observe  an  element  A  within  my  field  of 
vision,  and  investigate  its  connexion  with  another  ele- 
ment B  within  the  same  field,  I  step  out  of  the  domain 
of  physics  into  that  of  physiology  or  psychology,  pro- 


IN  TROD  UCTOR  Y  REMARKS.  17 

vided  Bj  to  use  the  apposite  expression  of  a  friend^  of 
mine  made  upon  seeing  this  drawing,  passes  through 
my  skin.  Reflexions  like  that  for  the  field  of  vision 
may  be  made  with  regard  to  the  province  of  touch  and 
the  perceptual  domains  of  the  other  senses. 

10. 

Reference  has  already  been  made  to  the  different 
character  of  the  groups  of  elements  designated  by 
ABC.  .  .  and  a /3 y.  As  a  matter  of  fact,  when  we 
see  a  green  tree  before  us,  or  remember  a  green  tree, 
that  is,  represent  a  green  tree  to  ourselves,  we  are  per- 
fectly aware  of  the  difference  of  the  two  cases.  The 
represented  tree  has  a  much  less  determinate,  a  much 
more  changeable  form  ;  its  green  is  much  paler  and 
more  evanescent ;  and,  what  is  of  especial  note,  it  is 
plainly  situate  in  a  different  domain.  A  movement 
that  -^e,  propose  to  execute  is  never  more  than  a  repre- 
sented movement,  and  appears  in  a  different  sphere 
from  that  of  the  executed  movement,  which  always 
takes  place  when  the  image  is  vivid  enough.  The  state- 
ment that  the  elements  A  and  a  appear  in  different 
spheres,  means,  if  we  go  to  the  bottom  of  it,  simply 
this,  that  these  elements  are  united  with  different  other 
elements.  Thus  far,  therefore,  the  fundamental  consti- 
tuents of  ABC.  .  .,  a  13 y .  .  .  would  seem  to  be  the 
same  (colors,  sounds,  spaces,  times,  motor  sensations 

IJ.  Popper  of  Vienna. 


z8  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

.  .  .),  and  only  the  character  of  their  connexion  differ- 
ent. 

Ordinarily  pleasure  and  pain  are  regarded  as  dif- 
ferent from  sensations.  Yet  not  only  tactile  sensa- 
tions, but  all  other  kinds  of  sensations,  may  pass 
gradually  into  pleasure  and  pain.  Pleasure  and  pain 
also  may  be  justly  termed  sensations.  Only  they  are 
not  so  well  analysed  and  so  familiar  as  the  common 
sensations.  In  fact,  sensations  of  pleasure  and  pain, 
however  faint  they  may  be,  really  make  up  the  con- 
tents of  all  so-called  emotions.  Thus,  perceptions, 
ideas,  volition,  and  emotion,  in  short  the  whole  inner 
and  outer  world,  are  composed  of  a  small  number  of 
homogeneous  elements  connected  in  relations  of  vary- 
ing evanescence  or  permanence.  Usually,  these  ele- 
ments are  called  sensations.  But  as  vestiges  of  a  one- 
sided theory  inhere  in  that  term,  we  prefer  to  speak 
simply  of  elements^  as  we  have  already  done.  The  aim 
of  all  research  is  to  ascertain  the  mode  of  connexion 
of  these  elements.^ 


II. 

That  in  this  complex  of  elements,  which  funda- 
mentally is  one^  the  boundaries  of  bodies  and  of  the 
ego  do  not  admit  of  being  established  in  a  manner 
definite  and  sufficient  for  all  cases,  has  already  been 
remarked.     The  comprehending  of  the  elements  that 

1  Compare  the  note  at  the  conclusion  of  my  treatise,  Die  Geschichte  und 
die  Wurteldes  Satzes  der  Erhaltung  dcr  Arbeit,  Prague,  Calve,  1872. 


INTR OD  UCTOR  Y  REMARKS.  19 

are  most  intimately  connected  with  pleasure  and  pain, 
under  one  ideal  mental-economical  unity,  the  ego,  is 
a  work  of  the  highest  significance  for  the  intellect  in 
the  functions  which  it  performs  for  the  pain-avoiding, 
pleasure-seeking  will.  The  delimitation  of  the  ego, 
therefore,  is  instinctively  effected,  is  rendered  familiar, 
and  possibly  becomes  fixed  through  heredity.  Owing 
to  their  high  practical  value,  not  only  for  the  individ- 
ual, but  for  the  entire  species,  the  composites  '*ego'* 
and  *'body"  assert  instinctively  their  claims,  and 
operate  with  all  the  power  of  natural  elements.  In 
special  cases,  however,  in  which  practical  ends  are  not 
concerned,  but  where  knowledge  is  an  object  in  itself, 
the  delimitation  in  question  may  prove  to  be  insuffi- 
cient, obstructive,  and  untenable.^ 

The  primary  fact  is  not  the  /,  the  ego,  but  the  ele- 
ments (sensations).  The  elements  constitute  the/.  I 
have  the  sensation  green,  signifies  that  the  element 
green  occurs  in  a  given  complex  of  other  elements  (sen- 
sations, memories).  When  /  cease  to  have  the  sensa- 
tion green,  when  /  die,  then  the  elements  no  longer 


^Similarly,  esprit  de  corps,  class  bias,  national  pride,  and  even  the  nar- 
rowest minded  local  patriotism  may  have  a  high  value,  y^r  r^r^a/« /wr/(7j^j 
But  such  attitudes  will  not  be  shared  by  the  broad-minded  inquirer,  at  least 
not  in  moments  of  research.  All  such  egoistic  views  are  adequate  only 
for  practical  purposes.  Of  course,  even  the  inquirer  may  succumb  to  habit. 
Trifling  pedantries  and  nonsensical  discussions,  the  cunnijig  appropriation 
of  others'  thoughts,  with  perfidious  silence  as  to  the  sources,  the  metaphorical 
dysphagia  suffered  when  recognition  must  be  givefa,  and  the  crooked  illu- 
mination of  others'  performances  when  this  is  done,  abundantly  show  that 
the  scientist  and  scholar  have  also  the  battle  of  existence  to  fight,  that  the 
ways  of  science  still  lead  to  the  mouth,  and  that  the/«r^  quest  of  knowledge 
in  our  present  social  conditions  is  still  an  ideal. 


20  THE  ANALYSIS  OF  THE  SENSATIONS. 

occur  in  their  ordinary,  familiar  way  of  association. 
That  is  all.  Only  an  ideal  mental-economical  unity, 
not  a  real  unity,  has  ceased  to  exist.  ^ 

If  a  knowledge  of  the  connexion  of  the  elements 
(sensations)  does  not  suffice  us,  and  we  ask.  Who  pos- 
sesses this  connexion  of  sensations.  Who  experiences 
the  sensations?  then  we  have  succumbed  to  the  habit  of 
subsuming  every  element  (every  sensation)  under  some 
unanalysed  complex,  and  we  are  falling  back  impercept- 
ibly upon  an  older,  lower,  and  more  limited  point  of 
view.* 


1  The  ego  is  not  a  definite,  unalterable,  sharply-bounded  unity.  None  of 
these  attributes  are  important;  for  all  vary  even  within  the  sphere  of  in- 
dividual life ;  in  fact  their  alteration  is  even  sought  after  by  the  individual. 
Continuity  alone  is  important.  This  view  accords  admirably  with  the  position 
which  Weismann  has  recently  reached  by  biological  investigations.  ("Zur 
Frage  der  Unsterblichkeit  der  Einzelligen,"  Biolog.  Centralbl.,  Vol.  IV.,  Nos. 
21,  22;  compare  especially  pages  654  and  655,  where  the  scission  of  the  indi- 
vidual into  two  equal  halves  is  spoken  of.)  But  this  continuity  is  only  a  means 
of  predisposing  and  of  conserving  what  is  contained  in  the  ego.  This  content 
and  not  the  ego  is  the  principal  thing.  This  content,  however,  is  not  confined 
to  the  individual.  With  the  exception  of  some  insignificant  and  valueless 
personal  memories,  it  remains  preserved  in  others  even  after  the  death  of  the 
individual.  The  ego  is  unsavable.  It  is  partly  the  knowledge  of  this  fact, 
partly  the  fear  of  it,  that  has  given  rise  to  the  many  extravagances  of  pessi- 
mism and  optimism,  and  to  numerous  religious  and  philosophical  absurdi- 
ties. In  the  long  run  we  shall  not  be  able  to  close  our  eyes  to  this  simple 
truth,  which  is  the  immediate  outcome  of  psychological  analysis.  We  shall 
then  no  longer  place  so  high  a  value  upon  the  ego,  which  even  during  the  in- 
dividual life  greatly  changes,  and  which,  in  sleep  or  during  absorption  in 
some  idea,  just  in  our  very  happiest  moments,  may  be  partially  or  wholly  ab- 
sent. We  shall  then  be  willing  to  renounce  individual  immortality,  and  not 
place  more  value  upon  the  subsidiary  elements  than  upon  the  principal  ones. 
In  this  way  we  shall  arrive  at  a  freer  and  more  enlightened  view  of  life,  which 
will  preclude  the  disregard  of  other  egos  and  the  over-estimation  of  our  own, 
[It  will  be  seen  from  the  above  remarks  that  I  consider  that  form  of  immor- 
tality alone  as  possessing  reality  and  worth,  which,  with  others.  Dr.  Paul 
Carus  upholds,  and  which  may  be  found  in  his  discussions  in  The  Monist, 
The  open  Court,  Fundaniental  Problems,  etc. — Mach,  1895.] 

2The  habit  of  treating  the  unanalysed  ego-complex  as  an  indiscerptible 
unity  frequently  a^^^tn^s  in  science  remarkable  forms.    First,  the  nervous 


INTRO D UCTOR  Y  REMARKS.  21 

The  so-called  unity  of  consciousness  is  not  an  argu- 
ment in  point.  Since  the  apparent  antithesis  of  real 
world  and  perceived  world  is  due  entirely  to  our  mode 
of  view,  and  no  actual  gulf  exists  between  them,  a  rich 
and  variously  interconnected  content  of  consciousness 
is  in  no  respect  more  difficult  to  understand  than  a 
rich  and  diversified  interconnexion  of  the  world. 

If  we  regard  the  ego  as  a  real  unity,  we  become  in- 
volved in  the  following  dilemma :  either  we  must  set 
over  against  the  ego  a  world  of  unknowable  entities 
(which  would  be  quite  idle  and  purposeless),  or  we 
must  regard  the  whole  world,  the  egos  of  other  people 
included,  as  comprised  in  our  own  ego  (a  proposition  to 
which  it  is  difficult  to  yield  serious  assent). 

But  if  we  take  the  ego  simply  as  a  practical  unity, 
put  together  for  purposes  of  provisional  survey,  or 

system  is  separated  from  the  body  as  the  seat  of  the  sensations.  In  the  ner- 
vous system  again,  the  brain  is  selected  as  the  organ  best  fitted  for  this  end, 
and  finally,  to  save  the  supposed  psychical  unity,  di point  is  sought  in  the  brain 
as  the  seat  of  the  soul.  But  such  crude  conceptions  are  hardly  fit  even  to 
foreshadovir  the  roughest  outlines  of  what  future  research  will  do  for  the  con- 
nexion of  the  physical  and  the  psychical.  The  fact  that  the  different  organs 
of  sensation  and  memory  are  physically  connected  with,  and  can  be  readily 
excited  by,  one  another,  is  probably  the  foundation  of  the  "psychical  unity." 

I  once  heard  the  question  seriously  discussed,  "How  the  percept  of  a 
large  tree  could  find  room  in  the  little  head  of  a  man  ? "  Now,  although  this 
"  problem  "  is  no  problem,  yet  it  renders  us  vividly  sensible  of  the  absurdity 
that  can  be  committed  by  thinking  sensations  spatially  into  the  brain.  When 
I  speak  of  the  sensations  of  another  person,  those  sensations  are,  of  course, 
not  exhibited  in  my  optical  or  physical  space;  they  are  mentally  added,  and 
I  conceive  them  causally,  not  spatially,  annexed  to  the  brain  observed  or 
represented.  When  I  speak  of  my  o^vn  sensations,  these  sensations  do  not 
exist  spatially  in  my  head,  but  rather  my  "  head"  shares  with  them  the  same 
spatial  field,  as  was  explained  above.     (Compare  the  remarks  on  Fig.  i.) 

[The  extent  to  which  the  old  notion  of  the  soul  still  pervades  modern 
physiological  research,  the  purpose  of  which  is  precisely  to  overcome  that 
ancient  view,  may  be  learned  from  Hauptmann's  Metaphysik  in  der  Physiologie^ 
Dresden,  1893,  with  whose  remarks  I  am  in  general  accord. — Mach.  1895.] 


22  THE  ANALYSIS  OF  THE  SENSATIONS, 

simply  as  a  more  strongly  coherent  group  of  elements, 
less  strongly  connected  with  other  groups  of  this  kind, 
questions  like  those  above  discussed  will  not  arise  and 
research  will  have  an  unobstructed  future. 

In  his  philosophical  notes  Lichtenberg  says  :  **  We 
become  conscious  of  certain  percepts  that  are  not  de- 
pendent upon  us  ;  of  others  that  we  at  least  think  are 
dependent  upon  us.  Where  is  the  border-line?  We 
know  only  the  existence  of  our  sensations,  percepts, 
and  thoughts.  We  should  say,  //  thinks^  just  as  we 
say,  //  lightens.  It  is  going  too  far  to  say  cogito,  if  we 
translate  cogito  by  /  think.  The  assumption,  or  pos- 
tulation,  of  the  ego  is  a  mere  practical  necessity." 
Though  the  method  by  which  Lichtenberg  arrived  at 
this  result  is  somewhat  different  from  ours,  we  must 
nevertheless  give  our  full  assent  to  his  conclusion. 

12. 

Bodies  do  not  produce  sensations,  but  complexes 
of  sensations  (complexes  of  elements)  make  up  bodies. 
If,  to  the  physicist,  bodies  appear  the  real,  abiding 
existences,  whilst  sensations  are  regarded  merely  as 
their  evanescent,  transitory  show,  the  physicist  for- 
gets, in  the  assumption  of  such  a  view,  that  all  bodies 
are  but  thought-symbols  for  complexes  of  sensations 
(complexes  of  elements).  Here,  too,  the  elements  form 
the  real,  immediate,  and  ultimate  foundation,  which  it 
is  the  task  of  physiological  research  to  investigate.  By 
the  recognition  of  this  fact,  many  points  of  psychology 


INTRODUCTORY  REMARKS. 


23 


and  physics  assume  more  distinct  and  more  economical 
forms,  and  many  spurious  problems  are  disposed  of. 
For  us,  therefore,  the  world  does  not  consist  of 
mysterious  entities,  which  by  their  interaction  with 
another,  equally  mysterious  entity,  the  ego,  produce 
sensations,  which  alone  are  accessible.  For  us,  colors, 
sounds,  spaces,  times,  .  .  .  are  the  ultimate  elements, 
whose  given  connexion  it  is  our  business  to  investi- 
gate.^    In  this  investigation  we  must  not  allow  our- 

II  have  always  felt  it  as  a  stroke  of  special  good  fortune,  that  early  in 
life,  at  about  the  age  of  fifteen,  I  lighted,  in  the  library  of  my  father,  on  a  copy 
of  Kant's  Prolegomena  zu  jeder  kiittftigen  Metaphysik.  The  book  made  at  the 
time  a  powerful  and  ineffaceable  impression  upon  me,  the  like  of  which  I 
never  afterward  experienced  in  any  of  my  philosophical  reading.  Some  two 
or  three  years  later  the  superfluous  role  played  by  "the  thing  in  itself" 
abruptly  dawned  upon  me.  On  a  bright  summer  day  under  the  open  heaven, 
the  world  with  my  ego  suddenly  appeared  to  me  as  one  coherent  mass  of  sensa- 
tions, only  more  strongly  coherent  in  the  ego.  Although  the  actual  working  out 
of  this  thought  did  not  occur  until  a  later  period,  yet  this  moment  was  deci- 
sive for  my  whole  view.  I  had  still  to  struggle  long  and  hard  before  I  was 
able  to  retain  the  new  conception  in  my  specialty.  With  the  valuable  parts  of 
physical  theories  we  necessarily  absorb  a  good  dose  of  false  metaphysics, 
which  it  is  very  difficult  to  sift  out  from  what  deserves  to  be  preserved,  espe- 
cially when  those  theories  have  become  very  familiar  to  us.  At  times,  too,  the 
traditional,  instinctive  views  would  arise  with  great  power  and  place  impedi- 
ments in  my  way.  Only  by  alternate  studies  in  physics  and  in  the  physiology 
of  the  senses,  and  by  historico-physical  investigations  (since  about  1863),  and 
after  having  endeavored  in  vain  to  settle  the  conflict  by  a  physico-psycho- 
logical  monadology,  have  I  attained  to  any  considerable  firmness  in  my  views. 
I  make  no  pretensions  to  the  title  of  philosopher.  I  only  seek  to  adopt  in 
physics  a  point  of  view  that  need  not  be  changed  the  moment  our  glance  is 
carried  over  into  the  domain  of  another  science ;  for,  ultimately,  all  must 
form  one  whole.  The  molecular  physics  of  to-day  certainly  does  not  meet 
this  requirement.  What  I  say  I  have  probably  not  been  the  first  to  say.  I 
also  do  not  wish  to  offer  this  exposition  of  mine  as  a  special  achievement. 
It  is  rather  my  belief  that  every  one  will  be  led  to  a  similar  view,  who  makes 
a  careful  survey  of  any  extensive  body  of  knowledge.  Avenarius,  with  whose 
works  I  recently  became  acquainted,  approaches  my  point  of  view  {Philosophic 
als  Denken  der  Welt  nach  dem  Princip  des  kleinsten  Kraftmasses,  1876).  Also 
Hering,  in  his  paper  on  Memory  {Almanach  der  Wiener  Akademie.  1870,  p.  258  ; 
English  translation,  O.  C.  Pub.  Co.,  Chicago,  1895),  and  J.  Popper  in  his  beau- 
tiful book.  Das  Recht  zn  leben  und  die  Pflicht  zu  sterben  (Leipsic,  1878,  p.  62), 
have  advanced  allied  thoughts.    Compare  also  my-  ^di^ev,  Ueber  die  Okono- 


24  THE  ANALYSIS  OF  THE  SENSATIONS. 

selves  to  be  impeded  by  such  intellectual  abridgments 
and  delimitations  as  body,  ego,  matter,  mind,  etc., 
which  have  been  formed  for  special,  practical  purposes 
and  with  wholly  provisional  and  limited  ends  in  view. 
On  the  contrary,  the  fittest  forms  of  thought  must  be 
created  in  and  by  that  research  itself,  just  as  is  done 
in  every  special  science.  In  place  of  the  traditional, 
instinctive  ways  of  thought,  a  freer,  fresher  view,  con- 
forming to  developed  experience,  must  be  substituted. 

13- 

Science  always  takes  its  origin  in  the  adaptation  of 
thought  to  some  definite  field  of  experience.  The  re- 
sults of  the  adaptation  are  thought-elements,  which 
are  able  to  represent  the  field.  The  outcome,  of 
course,  is  different,  according  to  the  character  and  ex- 
tent of  the  province  surveyed.  If  the  province  of  ex- 
perience in  question  is  enlarged,  or  if  several  provinces 
heretofore  disconnected  are  united,  the  traditional, 
familiar  thought-elements  no  longer  suffice  for  the  ex- 
tended province.  In  the  struggle  of  acquired  habit 
with  the  effort  after  adaptation,  problems  arise,  which 
disappear  when  the  adaptation  is  perfected,  to  make 
room  for  others  which  have  arisen  in  the  interim. 

To  the  physicist,  qud  physicist,  the  idea  of  "body" 

mische  Natur  der  physikalischen  Forschung  {Almanack  der  Wiener  Akademie^ 
1882,  p.  179,  note;  English  translation  in  n\y  Popular  Scientific  Lectures,  Chi- 
cago, 1895).  Finally  let  me  also  refer  here  to  the  introduction  to  W.  Preyer's 
Reine  Empfindungslehre  and  to  Riehl's  Freiburger  Antrittsrede,  p.  14.  I  should 
probably  have  much  additional  matter  to  cite  as  more  or  less  allied  to  this 
line  of  thought,  if  my  knowledge  of  the  literature  were  more  extensive, 


INTRODUCTORY  REMARKS.  25 

is  productive  of  a  real  facilitation  of  view,  and  is  not 
the  cause  of  disturbance.  So,  also,  the  person  with 
purely  practical  aims,  is  materially  assisted  by  the  idea 
of  the  /  or  ego.  For,  unquestionably,  every  form  of 
thought  that  has  been  designedly  or  undesignedly  con- 
structed for  a  given  purpose,  possesses  for  that  pur- 
pose a  permanent  value.  When,  however,  research  in 
physics  and  in  psychology  meets,  the  ideas  held  in  the 
one  domain  prove  to  be  untenable  in  the  other.  From 
the  attempt  at  mutual  adaptation  arise  the  various 
atomic  and  monadic  theories — which,  however,  never 
attain  their  end.  If  we  regard  sensations,  in  the  sense 
above  defined,  as  the  elements  of  the  world,  the  prob- 
lems referred  to  are  practically  disposed  of,  and  the 
Jirst  and  most  important  adaptation  effected.  This 
fundamental  view  (without  any  pretension  to  being  a 
philosophy  for  all  eternity)  can  at  present  be  adhered 
to  in  all  provinces  of  experience ;  it  is  consequently 
the  one  that  accommodates  itself  with  the  least  expen- 
diture of  energy,  that  is,  more  economically  than  any 
other,  to  the  present  temporary  collective  state  of  knowl- 
edge. Furthermore,  in  the  consciousness  of  its  purely 
economical  office,  this  fundamental  view  is  eminently 
tolerant.  It  does  not  obtrude  itself  into  provinces  in 
which  the  current  conceptions  are  still  adequate.  It 
is  ever  ready,  upon  subsequent  extensions  of  the  do- 
main of  experience,  to  yield  the  field  to  a  better  con- 
ception. 

The  philosophical  point  of  view  of  the  average 


26  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

man — if  that  term  may  be  applied  to  the  naive  realism 
of  the  ordinary  individual — has  a  claim  to  the  highest 
consideration.  It  has  arisen  in  the  process  of  im- 
measurable time  without  the  conscious  assistance  of 
man.  It  is  a  product  of  nature,  and  is  preserved  and 
sustained  by  nature.  Everything  that  philosophy  has 
accomplished — the  biological  value  of  every  advance, 
nay,  of  every  error,  admitted — is,  as  compared  with 
it,  but  an  insignificant  and  ephemeral  product  of  art. 
The  fact  is,  every  thinker,  every  philosopher,  the  mo- 
ment he  is  forced  to  abandon  his  narrow  intellectual 
province  by  practical  necessity,  immediately  returns 
to  the  universal  point  of  view  held  by  all  men  in  com- 
mon.^ 

To  discredit  this  point  of  view  is  not  then  the  pur- 
pose of  the  foregoing  ''introductory  remarks."  The 
task  which  we  have  set  ourselves  is  simply  to  show  why 
and  to  what  purpose  ior  the  greatest  portion  of  life  we 
hold  it,  and  w/iy  and  for  what  purpose  we  are  provisorily 
obliged  to  abandon  it.  No  point  of  view  has  absolute, 
permanent  validity.  Each  has  importance  only  for 
some  given  end.* 

l[Molifere'8  scourged  philosopher  {in  L^  Martag^e /bred)  does  not  say,  It 
seems  to  me  that  I  am  pummelled,  but,  I  am  pummelled.— 1895.] 

2  [A  kindred  view  will  be  found  in  Avenarius  {Kritik  der  reinen  Er/ah- 
rung,  and  Der  menschliche  IVeltbegriff).  Avenarius  has  also  undertaken  the 
commendable  task  of  explaining  the  development  of  philosophy  on  the  basis 
of  the  facts  furnished  by  the  history  of  civilisation.  For  a  further  develop- 
ment of  this  view,  which  was  evoked  by  a  correspondence  with  Dr.  Paul 
Carus,  see  the  Appendix  to  this  volume.— 1895.] 


THE    CHIEF   POINTS    OF   VIEW    FOR 

THE  INVESTIGATION  OF  THE 

SENSES. 


I. 

TT  TE  WILL  now  take,  from  the  point  of  view  at- 
*  »     tained,  a  broad  and  general  survey  of  the  special 
problems  that  will  engage  our  attention. 

When  once  the  inquiring  intellect  has  gained, 
through  adaptation,  the  habit  of  connecting  two 
things,  A  and  B,  in  thought,  it  always  thereafter  seeks 
to  retain  this  habit,  even  where  the  circumstances  are 
slightly  altered.  Wherever  A  makes  its  appearance, 
B  is  added  in  thought.  The  principle  here  formulated, 
which  has  its  root  in  an  effort  for  economy,  and  is  par- 
ticularly noticeable  in  the  work  of  great  investigators, 
may  be  termed  the  principle  of  continuity. 

Every  observed  variation  in  the  connexion  of  A 
and  B  which  is  sufficiently  large  to  be  noticed  makes 
itself  felt  as  a  disturbance  of  the  above-mentioned 
habit,  and  continues  to  do  so  until  the  latter  is  suffi- 
ciently modified  to  eliminate  the  disturbance.  We 
have  become  accustomed  to  seeing  light  deflected  in 


28  THE  ANALYSIS  OF  THE  SENSATIONS. 

passing  from  air  to  glass,  and  vice  versa.  But  the  de- 
flexion differs  noticeably  in  different  cases,  and  the 
habit  gained  in  some  cases  cannot  be  carried  over  un- 
disturbed to  new  cases,  until  we  are  prepared  to  asso- 
ciate with  every  particular  angle  of  incidence  a  par- 
ticular angle  of  refraction — a  condition  satisfied  by 
the  discovery  of  the  so-called  law  of  refraction,  or  by 
acquirement  of  familiarity  with  the  rule  contained  in 
the  same.  Thus  another  and  modifying  principle  con- 
fronts that  of  continuity ;  we  will  call  it  the  principle 
of  sufficient  determinateness,  or  sufficient  differentiation. 

The  joint  action  of  the  two  principles  may  be  very 
well  illustrated  by  a  further  analysis  of  the  example 
cited.  In  order  to  deal  with  the  phenomena  exhibited 
in  the  change  of  color  of  light,  the  idea  of  the  law  of 
refraction  must  still  be  retained,  but  with  every  par- 
ticular color  a  particular  index  of  refraction  must  be 
associated.  We  soon  perceive  that  with  every  par- 
ticular temperature  also,  a  particular  index  of  refrac- 
tion must  be  associated ;  and  so  on. 

In  the  end,  this  process  leads  to  temporary  con- 
tentment and  satisfaction,  the  two  things  A  and  B 
being  conceived  as  so  connected  that  to  every  observ- 
able change  of  the  one  there  corresponds  a  dependent 
change  of  the  other.  It  may  happen  that  A  as  well 
as  B  is  conceived  as  a  complex  of  components,  and 
that  to  every  particular  component  of  A  a  particular 
component  of  B  corresponds.  This  occurs,  for  ex- 
ample, when  B  IS  di.  spectrum,  and  A  the  correspond- 


CHIEF  POINTS  OF  VIEW.  29 

ing  sample  of  a  compound  to  be  tested,  in  which  case 
to  every  component  part  of  the  spectrum  one  of  the 
components  of  the  matter  volatilised  before  the  spec- 
troscope is  referred,  independently  of  the  others.  Only 
through  complete  familiarity  with  this  relation  can  the 
principle  of  sufficient  determinateness  be  satisfied. 

2. 

Suppose,  nov7,  that  we  are  considering  a  color- 
sensation  B^  not  in  its  dependence  on  A^  the  heated 
matter  tested,  but  in  its  dependence  on  the  elements 
of  the  retinal  process,  N.  In  such  case,  not  the  kind 
but  only  the  direction  of  the  investigation  is  changed. 
None  of  the  preceding  observations  lose  their  force, 
and  the  principles  to  be  followed  remain  the  same. 
And  this  holds  good,  of  course,  of  all  sensations. 

Now,  sensation  may  be  analysed  in  itself,  imme- 
diately, that  is,  psychologically  (which  was  the  course 
adopted  by  Johannes  Miiller),  or  the  co-ordinate  physi- 
cal (physiological)  processes  may  be  investigated  ac- 
cording to  the  methods  of  physics  (the  course  usually 
preferred  by  the  modern  school  of  physiologists),  or, 
finally,  the  connexion  of  psychologically  observable 
data  with  the  corresponding  physical  (physiological) 
processes  may  be  followed  up — a  mode  of  procedure 
which  will  carry  us  farthest,  since  in  this  method  ob- 
servation is  directed  to  all  sides,  and  one  investigation 
serves  to  support  the  other.  We  shall  endeavor  to  attain 
this  last-named  end  wherever  it  appears  practicable. 


30  THE  ANALYSIS  OF  THE  SENSATIONS. 

This  being  our  object,  then,  it  is  evident  that  the 
principle  of  continuity  and  that  of  sufficient  determi- 
nateness  can  be  satisfied  only  on  the  condition  that 
with  the  same  B  (this  or  that  sensation)  is  always  as- 
sociated the  same  N  (the  same  nerve-process),  and  for 
every  observable  change  of  ^  a  corresponding  change 
of  N  is  discoverable.  If  B  is  psychologically  analysa- 
ble  into  a  number  of  independent  components,  then 
we  shall  rest  satisfied  only  on  the  discovery,  in  N,  of 
such  components  as  correspond  to  the  former.  In  a 
word,  for  all  psychically  observable  details  of  B  we 
have  to  seek  the  corresponding  physical  details  of  N. 

We  may  thus  establish  a  guiding  principle  for  our 
investigations,  which  may  be  termed  the  principle  of 
the  complete  parallelism  of  the  psychical  and  physical. 
According  to  our  fundamental  conception,  which  rec- 
ognises no  gulf  between  the  two  provinces  (the  psychi- 
cal and  the  physical),  this  principle  is  almost  a  matter 
of  course ;  but  we  may  also  enunciate  it,  as  I  did  years 
ago,  without  the  help  of  this  fundamental  conception, 
as  a  heuristic  principle  of  research.^ 


As  the  principle  is  stated  in  rather  abstract  form, 
a  few  concrete  examples  may  now  be  given.  Wherever 

1  Compare  my  paper,  Ueber  die  Wirkung  der  rSumlichen  Vertheilung  des 
Lichtreizes  au/die  Netzhaut  {Sitzungsberichte  der  Wiener  Akademie,  Vol.  LIL, 
1865);  tuvihex  Reichert' s  und  Dubois'  Arckiv,  18G5,  p.  634,  and  Grundlinien  der 
Lehre  von  den  Bevjegungsempfindungen  (Leipsic  :  Engelmann,  1875,  p.  63).  The 
principle  is  also  implicitly  contained  in  an  article  pf  va\.ii&iaY\Q.h.\.e'^Zeit- 
schri/tfUrPhilosophie,  Vol.  XLVI.,  1865,  p.  5. 


CHIEF  POINTS  OF  VIEW.  31 

I  have  a  sensation  of  space,  whether  through  the  sen- 
sation of  sight  or  through  that  of  touch,  or  in  any  other 
way,  I  am  obliged  to  assume  the  presence  of  a  nerve- 
process  in  all  cases  the  same  in  kind.  For  all  time- 
sensations,  also,  I  must  suppose  like  nerve-processes. 
If  I  see  figures  which  are  the  same  in  size  and  shape 
but  differently  colored,  I  seek,  in  connexion  with  the 
different  color-sensations,  certain  identical  space-sen- 
sations with  their  appurtenant  identical  nerve-pro- 
cesses. If  two  figures  are  similar  (that  is,  if  they  yield 
partly  identical  space-sensations)  then  the  appurtenant 
nerve-processes  contain  partly  identical  components. 
If  two  different  melodies  have  the  same  rhythm,  then, 
side  by  side  with  the  different  tone-sensations  exists  in 
both  cases  an  identical  time-sensation  with  identical 
appurtenant  nerve-processes.  If  two  melodies  of  dif- 
ferent pitch  are  identical,  then  the  tone-sensations  as 
well  as  their  physical  conditions,  have,  in  spite  of  the 
different  pitch,  identical  constituents.  If  the  seem- 
ingly limitless  multiplicity  of  color-sensations  is  sus- 
ceptible of  being  reduced,  by  psychological  analysis 
(self-observation),  to  six  elements  (fundamental  sen- 
sations), a  like  simplification  may  be  expected  for  the 
system  of  nerve-processes.  If  our  system  of  space-sen- 
sations appears  in  the  character  of  a  threefold  mani- 
foldness,  its  system  of  co-ordinated  nerve-processes 
will  likewise  present  itself  as  such. 


32  THE  ANALYSIS  OF  THE  SENSATIONS. 


This  principle  has,  moreover,  always  been  more  or 
less  consciously,  more  or  less  consistently,  followed. 

For  example,  when  Helmholtz  assumes  for  every 
tone-sensation  a  special  nerve-fibre  in  the  ear  (with  its 
appurtenant  nerve-process),  when  he  resolves  clangs, 
or  compound  sounds,  into  tone-sensations,  when  he 
refers  the  affinity  of  compound  tones  to  the  presence 
of  like  tone- sensations  (and  nerve- processes),^  we  have 
in  this  method  of  procedure  a  practical  illustration  of 
our  principle.  Merely  its  application  is  not  complete, 
as  will  be  later  shown.  Brewster ,2  guided  by  a  psycho- 
logical but  defective  analysis  of  color-sensations,  and 
by  imperfect  physical  experiments,^  was  led  to  the  view 
that,  corresponding  to  the  three  sensations,  red,  yellow, 
and  blue,  there  existed  likewise  physically  only  three 
kinds  of  light,  and  that,  therefore,  Newton^s  assump- 
tion of  an  unlimited  number  of  kinds  of  light,  with  a 
continuous  series  of  refractive  indices,  was  erroneous. 

1  Helmholtz,  Die  Lekre  von  den  Tonempfindungen.  Braunschweig :  Vie- 
weg,  1863.  English  translation  by  Alex.  J.  Ellis.  London  :  Longmans,  Green, 
&  Co. 

2  Brewster,  >4  Treatise  on  Optics, 'Loudon,  1831.  Brewster  regarded  the 
red,  yellow,  and  blue  light  as  extending  over  the  whole  solar  spectrum, 
though  distributed  there  with  varying  intensity,  so  that,  to  the  eye,  red  ap- 
pears at  both  ends  (the  red  and  the  violet),  yellow  in  the  middle,  and  blue  at 
the  end  of  greater  refrangibility. 

SBrewster  believed  that  he  was  able  to  alter  by  absorption  the  nuances  of 
the  spectrum— colors  regarded  by  Newton  as  simple — a  result  which,  if  cor- 
rect, would  really  destroy  the  Newtonian  conception.  He  experimented, 
however,  as  Helmholtz  [^Physiological  Optics)  has  shown,  with  an  impure 
spectrum. 


CHIEF  POINTS  OF  VIEW.  33 

Brewster  might  easily  fall  into  the  error  of  regarding 
green  as  a  compound  sensation.  But  had  he  reflected 
that  color-sensation  may  make  its  appearance  entirely 
without  physical  light,  he  would  have  confined  his  con- 
clusions to  the  nerve-process  and  left  untouched  New- 
ton's assumptions  in  the  province  of  physics,  which  are 
as  well  founded  as  his  own.  Thomas  Young  corrected 
this  error.  He  perceived  that  an  unlimited  number  of 
kinds  of  physical  light  with  an  uninterrupted  series  of 
refractive  indices  (and  wave-lengths)  were  compatible 
with  a  small  number  of  color-sensations  and  nerve- 
processes,  that  a  discrete  number  of  color-sensations 
did  answer  to  the  continuum  of  deflexions  in  the  prism 
(to  the  continuum  of  the  space-sensations).  But  even 
Young  did  not  apply  the  principle  with  full  conscious- 
ness or  strict  consistency,  wholly  apart  from  the  fact 
that  he  allowed  himself  to  be  misled,  in  his  psycho- 
logical analysis,  by  physical  prejudices.  Young,  too, 
first  assumed,  as  fundamental  sensations,  red,  yellow, 
and  blue,  for  which  he  later  substituted  red,  green, 
and  violet — misled,  as  Alfred  Mayer,  of  Hoboken,  has 
admirably  shown, ^  by  a  physical  error  of  Wollaston's. 

\ Philosophical  Magazine,  February,  1876,  p.  iii.  Wollaston  was  the  first 
to  notice  (1802)  the  dark  lines  of  the  spectrum,  later  named  after  Fraunhofer, 
and  believed  that  he  saw  his  narrow  spectrum  divided  by  the  strongest  of 
these  lines  into  a  red,  a  green,  and  a  violet  part.  He  regarded  these  lines  as 
the  dividing  lines  of  the  physical  colors.  Young  took  up  this  conception,  and 
substituted  for  his  fundamental  sensations  red,  yellow,  and  blue,  the  colors 
red,  green,  and  violet.  In  his  first  conception,  Young  regarded  green  as  a 
composite  sensation,  in  his  second,  both  green  and  violet  as  simple.  The 
questionable  results  which  psychological  analysis  may  thus  yield,  are  well 
calculated  to  destroy  belief  in  its  usefulness  in  general.  But  we  must  not  for- 
get that  there  is  no  principle  in  the  application  of  which  error  is  excluded. 


34  THE  ANALYSIS  OF  THE  SENSATIONS. 

The  direction  in  which  the  theory  of  color-sensation, 
which  has  reached  a  high  degree  of  perfection  through 
Hering,  has  still  to  be  modified,  was  pointed  out  by 
me  many  years  ago  in  another  place.  ^ 

Here,  too,  practice  is  determinative.  The  circumstance  that  the  physical 
conditions  of  sensation  almost  always  give  rise  to  composite  sensations, 
and  that  the  components  of  sensation  seldom  make  their  appearance  sepa- 
rately, renders  psychological  analysis  very  difficult.  Thus,  green  is  a  simple 
sensation;  a  given  pigment  or  spectrum  green,  however,  will  as  a  rule  excite 
also  a  concomitant  yellow  or  blue  sensation,  and  thus  favor  the  erroneous 
idea  (based  upon  the  results  of  pigment-mixing)  that  the  sensation  of  green  is 
compounded  of  yellow  and  blue.  Careful  physical  study,  therefore,  is  also 
an  indispensable  requisite  of  psychological  analysis.  On  the  other  hand, 
physical  observation  must  not  be  overestimated.  The  mere  observation  that 
a  yellow  and  blue  pigment  mixed,  yield  a  green  pigment,  cannot  alone  deter- 
mine the  perception  of  yellow  and  blue  in  green,  unless  one  or  the  other  color 
is  actually  contained  in  it.  Certainly  no  one  sees  yellow  and  blue  in  white, 
although,  as  a  fact,  spectrum-yellow  and  spectrum-blue  mixed  give  white. 

II  will  here  condense  into  a  note  what  I  have  to  say  concerning  the  treat- 
ment of  the  theory  of  color-sensation.  We  frequently  meet  with  the  asser- 
tion, in  recent  works,  that  the  six  fundamental  color-sensations,  white,  black, 
red,  green,  yellow,  blue,  which  Hering  adopted,  were  first  proposed  by  Leo- 
nardo da  Vinci,  and  later  by  Mach  and  Aubert.  That  the  assertion  with  re- 
gard to  Leonardo  da  Vinci  was  founded  upon  an  error  appeared  to  me,  from 
the  very  first,  in  view  of  the  conceptions  prevalent  at  his  time,  highly  prob- 
able. Let  us  hear  what  he  himself  says  in  his  Book  of  Painting  (Nos.  254 
and  255  in  the  translation  of  Heinrich  Ludwig,  Quellenschri/ten  zur  Kunst- 
geschickte,  Vienna,  BraumQller,  1882,  Vol.  XVIII).  "254.  Of  simple  colors 
there  are  six.  The  first  of  these  is  v/hite,  although  philosophers  admit  nei- 
ther white  nor  black  into  the  number  of  colors,  since  the  one  is  the  cause  of 
colors,  the  other  of  their  absence.  But,  inasvtuch  as  the  painter  cannot  do 
without  them,  we  shall  include  these  two  also  among  the  other  colors  and  say 
that  white  in  this  classification  is  the  first  among  the  simple  colors,  yellow 
the  second,  green  the  third,  blue  the  fourth,  red  the  fifth,  black  the  sixth. 
And  the  white  we  will  let  represent  the  light,  without  which  one  can  see  no 
color,  the  yellow  the  earth,  the  green  the  water,  blue  the  air,  red  fire,  and 
black  the  darkness  which  is  found  above  the  element  of  fire,  because  in  that 
place  there  is  no  matter  or  solid  substance  upon  which  the  sunbeams  can 
exert  their  force,  and  which  as  a  result  they  might  illumine."  "255.  Blue 
and  green  are  not  simple  colors  by  themselves.  For  blue  is  composed  of  light 
and  darkness,  as,  the  blue  of  the  air,  which  is  made  up  of  the  most  perfect 
black  and  perfectly  pure  white."  "Green  is  composed  of  a  simple  and  a 
composite  color,  namely,  of  yellow  and  blue."  This  will  suffice  to  show  that 
Leonardo  da  Vinci  is  concerned  partly  with  observations  concerning  pig- 
ments, partly  with  conceptions  of  natural  philosophy,  but  not  with  the  subject 
of  fundamental  color-sensations.  The  many  remarkable  and  subtle  scientific 
observations  of  all  sorts. which  are  coptain?^  in  LepnarijQ  dji  yjpgi's.  book 


CHIEF  POINTS  OF  VIEW,  35 

The  examples  adduced  will  suffice  to  explain  the 
significance  of  the  above-enunciated  principle  of  in- 
quiry, and  at  the  same  time  to  show  that  this  principle 
is  not  entirely  new.  In  formulating  the  principle, 
years  ago,  I  had  no  other  object  than  that  of  setting 
clearly  before  ttiy  own  mind  a  truth  which  I  had  long 
instinctively  felt. 


As  we  recognise  no  real  gulf  between  the  physical 
and  the  psychical,  it  is  a  matter  of  course  that,  in  the 
study  of  the  sense-organs,  general  physical  as  well  as 
special   biological    observations    may   be    employed. 

lead  to  the  conviction  that  the  artists,  and  among  them  especially  he  himself, 
were  the  true  forerunners  of  the  great  scientists  who  came  soon  afterwards. 
These  men  were  obliged  to  understand  nature  in  order  to  reproduce  it  agree- 
ably ;  they  observed  themselves  and  others  in  the  interest  of  pure  pleas- 
ure. Yet  Leonardo  was  far  from  being  the  author  of  all  the  discoveries  and 
inventions  which  Groth,  for  example,  {Leonardo  da  Vinci  ah  Ingenieur  und 
Philosophy  Berlin,  1874,)  ascribes  to  him.  My  own  scattered  remarks  concern- 
ing the  theory  of  color-sensation,  were  perfectly  clear.  I  assumed  the  funda- 
mental sensations  white,  black,  red,  yellow,  green,  blue,  and  six  different 
corresponding  (chemical)  processes  (not  nerve-fibres)  in  the  retina.  (Com- 
pare ReicherVs  und  Dubois''  Archiv,  1865,  p.  633,  et  seq.)  As  a  physicist,  I  was 
of  course  familiar  with  the  relation  of  the  complementary  colors.  My  conr 
ception,  however,  was  that  the  two  complementary  processes  together  excited 
a  new — the  white — process.  [Loc.  cit.,  p.  634.)  I  gladly  acknowledge  the  great 
advantages  of  Hering's  theory.  They  consist  for  me  in  the  following.  First, 
the  black  process  is  regarded  as  a  reaction  opposing  the  white  process ;  I  can 
appreciate  all  the  more  the  facilitation  involved  in  this  conception,  as  it  was 
just  the  relation  of  black  and  white  that  for  me  presented  the  greatest  diffi- 
culty. Further,  red  and  green,  as  also  yellow  and  blue,  are  regarded  as  an- 
tagonistic processes  which  do  not  produce  a  new  process,  but  mutually  anni- 
hilate each  other.  According  to  this  conception  white  is  not  subsequently 
produced  but  is  already  present  beforehand,  and  still  remains  on  the  annihi- 
lation of  a  color  by  the  complementary  color.  The  only  point  that  still  dis- 
satisfies me  in  Hering's  theory  is  that  it  is  difficult  to  perceive  why  the  two 
opposed  processes  of  black  and  white  may  be  simultaneously  produced  and 
simultaneously  felt,  while  such  is  not  the  case  with  red-green  and  blue-yel- 
low. Compare  also  my  paper,  previously  cited,  in  the  Sitzungsberichte  der 
.}Fiener.Akademief  Yq},  :^,  18&5,  October. ..^., 


36  THE  ANALYSIS  OF  THE  SENSATIONS. 

Much  that  appears  to  us  difficult  of  comprehension 
when  we  draw  a  parallel  between  a  sense-organ  and  a 
physical  apparatus,  is  rendered  quite  obvious  in  the 
light  of  the  theory  of  evolution,  simply  by  assuming 
that  we  are  concerned  with  a  living  organism  with  par- 
ticular memories,  particular  habits  and  manners,  which 
owe  their  origin  to  a  long  and  eventful  race-history. 
I  shall  condense  what  I  have  to  say  on  this  subject 
into  a  footnote  of  some  length.^     Even  teleological 

IThe  idea  of  applying  the  theory  of  evolution  to  physiology  in  general, 
and  to  the  physiology  of  the  senses  in  particular,  was  advanced,  prior  to  Dar- 
win, by  Spencer  {1855).  It  received  an  immense  impetus  through  Darwin's 
book  The  Expression  of  the  Emotions.  Later,  Schuster  discussed  the  question 
whether  there  were  "inherited  ideas"  in  the  Darwinian  sense.  I,  too,  ex- 
pressed myself  in  favor  of  the  application  of  the  idea  of  evolution  to  the  the- 
ory of  the  sense-organs  {Sitzungsberichte  der  Wiener  Akademie,  October,  1866). 
One  of  the  finest  and  most  instructive  discussions,  in  the  way  of  a  psycholo- 
gico-physiological  application  of  the  theory  of  evolution,  is  to  be  found  in  the 
Academic  Anniversary  Address  of  Hering,  On  Memory  as  a  General  Function 
0/  Organised  Matter,  1870,  (English  translation.  Open  Court  Publishing  Com- 
pany, Chicago,  1895).  As  a  fact,  memory  and  heredity  are  nearly  embraced 
under  one  concept  if  we  reflect  that  organisms,  which  were  part  of  the  parent- 
body,  emigrate  and  become  the  basis  of  new  individuals.  Heredity  is  ren- 
dered almost  as  intelligible  to  us  by  this  thought  as,  for  example,  is  the  fact 
that  Americans  speak  English,  or  that  their  state-institutions  much  resemble 
the  English,  etc.  The  problem  involved  in  the  fact  that  organisms  possess 
memory,  a  property  which  is  apparently  lacking  to  inorganic  matter,  is,  of 
course,  not  removed  by  this  insight,  but  still  exists. — Recently  Weismann 
(Ueber  die  Dauer  des  Lebens)  has  conceived  death  as  a  phenomenon  of  hered- 
ity. This  admirable  book,  also,  contributes  greatly  to  our  enlightenment. 
The  difficulty  which  might  be  found  in  the  fact  that  a  trait  which  can  make 
its  appearance  in  the  parent-organism  only  after  the  process  of  inheritance  is 
ended  should  be  subject  to  inheritance,  lies  probably  only  in  the  manner  of 
statement.  It  disappears  when  we  consider  that  the  power  of  the  cells  of  the 
body  to  multiply  can  increase,  as  Weismann  shows,  only  at  the  cost  of  the 
increase  of  the  germ-cells.  Accordingly,  we  may  say  that  greater  length  of 
life  on  the  part  of  the  cell-society  and  lessened  propagation  are  two  phenom- 
ena which  mutually  condition  each  other. — While  a  student  at  the  Gymna- 
sium, I  heard  it  stated  that  plants  from  the  Southern  Hemisphere  bloom 
in  our  latitudes,  when  it  is  spring  in  their  native  place.  I  recall  clearly  the 
mental  shock  which  this  communication  caused  me.  If  it  is  true,  we  have 
actually  a  case  of  plant-memory.  The  so-called  reflex  actions  of  animals  may 
be  explained  in  a  natural  manner  as  phenomena  of  memory  outside  the  organ 


CHIEF  POINTS  OF  VIEW.  37 

conceptions,  as  aids  to  investigation,  are  not  to  be 
shunned.  It  is  true,  our  comprehension  of  the  facts 
of  reality  is  not  enhanced  by  referring  them  to  an  un- 

of  consciousness.  I  was  a  witness  of  a  very  remarkable  phenomenon  of  this 
kind— in  1865,  I  think — with  RoUett,  who  was  experimenting  with  pigeons 
whose  brains  had  been  removed.  These  animals  drank  whenever  their  feet 
were  placed  in  a  cold  liquid,  whether  the  latter  was  water,  mercury,  or  sul- 
phuric acid.  Now  since  a  bird  must  ordinarily  wet  its  feet  when  it  seeks  to 
quench  its  thirst,  the  conception  arises  quite  naturally  that  we  have  to  do 
here  with  a  habit  adapted  to  an  end,  which  is  conditioned  by  the  mode  of  life 
and  fixed  by  inheritance,  and  which,  even  when  consciousness  is  eliminated, 
takes  place  with  the  precision  of  clock-work  on  the  application  of  the  stim- 
ulus appropriate  to  its  excitation.  Goltz,  in  his  remarkable  book  Die  Nerven- 
centren  des  Frosches,  and  in  later  writings,  has  described  many  phenomena  of 
the  sort. — I  will  relate,  also,  in  this  connexion,  some  other  experiences  which 
I  recall  with  a  great  deal  of  pleasure.  In  the  autumn  vacation  of  1873,  my 
little  boy  brought  me  a  sparrow  a  few  days  old,  which  had  fallen  from  its 
nest,  and  desired  to  raise  it.  But  the  matter  was  not  so  easy.  The  little  ani- 
mal could  not  be  induced  to  swallow,  and  would  certainly  soon  have  fallen  a 
victim  to  the  indignities  that  would  have  been  unavoidable  in  feeding  it  by 
force.  I  then  fell  into  the  following  train  of  thought:  "  Whether  or  not  the 
Darwinian  theory  is  correct,  the  new-born  child  would  certainly  perish  if  it 
had  not  the  perfected  organs  and  inherited  impulse  to  suck,  which  are  brought 
into  activity  quite  automatically  and  mechanically  by  the  appropriate  exci- 
tation. Something  similar  (in  another  form)  must  exist  likewise  in  the  case 
of  the  bird."  I  exerted  myself  to  discover  the  appropriate  excitation.  A 
small  insect  was  stuck  upon  a  sharp  stick  and  swung  rapidly  about  the  head 
of  the  bird.  Immediately  the  bird  opened  its  bill,  beat  its  wings,  and  eagerly 
devoured  the  proffered  food.  I  had  discovered  the  right  excitation  for  setting 
the  impulse  and  the  automatic  movement  into  activity.  The  animal  grew  per- 
ceptibly stronger  and  greedier,  it  began  to  snatch  at  the  food,  and  once  seized 
an  insect  that  had  accidentally  fallen  from  the  stick  to  the  table;  from  that 
time  on  it  ate,  without  ceremony,  of  itself.  In  proportion  as  its  intellect  de- 
veloped, the  required  amount  of  excitation  decreased.  On  reaching  inde- 
pendence, the  animal  took  on,  little  by  little,  all  the  characteristic  ways  of 
sparrows,  which  it  certainly  had  not  learnt  by  itself.  By  day  (during  full  in- 
tellectual activity)  it  was  very  trustful  and  friendly.  In  the  evening,  other 
phenomena  were  exhibited.  The  creature  grew  timid.  It  always  sought  out 
the  highest  places  in  the  room,  and  would  become  quiet  only  when  it  was 
prevented  by  the  ceiling  from  going  higher.  Here  again  we  have  an  inherited 
habit  adapted  to  an  end.  On  the  coming  of  darkness,  the  demeanour  of  the 
animal  changed  totally.  When  approached,  it  ruffled  its  feathers,  began  to 
hiss,  and  showed  every  appearance  of  terror  and  real  physical  fear  of  ghosts. 
Nor  is  this  fear  without  its  reasons  and  its  purpose  in  a  creature  which,  under 
normal  circumstances,  may  at  any  moment  be  devoured  by  some  monster. 

This  last  observation  strengthened  me  in  an  opinion  already  formed,  that 
the  superstition  of  my  children  did  not  have  its  source  in  nursery  tales,  which 
were  carefully  excluded  from  them,  but  was  innate.    One  of  my  children 


38  THE  ANALYSIS  OF  THE  SENSATIONS. 

known  World-Purpose,  itself  problematic.  Neverthe- 
less, the  question  as  to  the  value  that  a  given  function 
has  for  the  existence  of  an  organism,  or  as  to  what  are 

would  regard  with  anxiety  an  arm-chair,  which  stood  in  the  shadow;  another 
carefully  avoided,  in  the  evening,  a  coal-hod  by  the  stove,  especially  when 
this  stood  with  raised  cover,  resembling  open  jaws.  The  fear  of  spirits  is  the 
true  mother  of  religions.  Neither  scientific  analysis  nor  the  careful  histori- 
cal criticism  of  a  David  Strauss,  as  applied  to  myths,  which,  for  the  strong 
intellect,  are  refuted  even  before  they  are  invented,  will  all  at  once  do  away 
with  and  banish  these  things.  Habits  which  have  so  long  answered,  and  in-  a 
measure  still  answer,  to  actual  economic  needs  (fear  of  a  worse,  hope  of  a 
better),  will  long  continue  to  exist  in  mysterious  and  uncontrollable  instincts 
of  the  brain.  Just  as  the  birds  on  uninhabited  islands  (according  to  Darwin) 
learn  the  fear  of  man  only  after  the  lapse  of  generations,  so  we  shall  unlearn, 
only  after  many  generations,  that  useless  habit  known  as  the  creeping  of  flesh. 
Every  presentation  of  Faust  may  teach  us  the  extent  to  which  we  are  still  in 
secret  sympathy  with  the  conceptions  of  the  age  of  witchcraft.— I  will  here 
relate  one  other  curious  fact,  for  the  knowledge  of  which  I  am  indebted  to  my 
father  (an  enthusiastic  Darwinian  and  in  the  latter  part  of  his  life  land-pro- 
prietor in  Carniola).  My  father  occupied  himself  much  with  silk-culture, 
raised  the  yami-mai  in  the  open  oak  woods,  etc.  The  ordinary  mulberry  silk- 
worm has,  for  many  generations,  been  raised  indoors,  and  has  become  ex- 
ceedingly helpless  and  dependent.  When  the  time  for  passing  into  the  chry- 
salic  state  arrives,  it  is  the  custom  to  give  the  creatures  bundles  of  straw, 
upon  which  they  spin  their  cocoons.  Now  it  one  day  occurred  to  my  father 
not  to  prepare  the  usual  bundles  of  straw  for  a  colony  of  silk-worms.  The 
result  was  that  the  majority  of  the  worms  perished,  and  only  a  small  portion, 
the  geniuses  (those  with  the  greatest  power  of  adaptation)  spun  their  cocoons. 
Whether,  as  my  sister  believes  she  has  observed,  the  experiences  of  one  gene- 
ration are  utilised,  in  noticeable  degree,  in  the  very  next  generation,  is  a  ques- 
tion which  must  probably  be  left  to  further  investigation.— From  all  these  re- 
markable phenomena  we  need  derive  no  mysticism  of  the  Unconscious.  A 
memory  reaching  beyond  the  individual  renders  them  intelligible. — A  psy- 
chology in  the  Spencer-Darwinian  sense,  founded  upon  the  theory  of  evolu- 
tion, but  supported  by  positive  investigation  of  particulars,  would  yield  richer 
results  than  all  previous  speculation  has  done. — These  observations  and  con- 
ceptions had  long  been  made  and  written  down  when  Schneider's  valuable 
work,  Der  thierische  Wille,  Leipsic,  1880,  which  contains  many  that  are  simi- 
lar, made  its  appearance.  I  agree  with  the  details  of  Schneider's  discussions 
almost  throughout,  although  his  fundamental  conceptions  in  the  realms  of  nat- 
ural science  with  regard  to  the  relation  of  sensation  and  physical  process,  the 
significance  of  the  survival  of  species,  etc.,  are  essentially  different  from 
mine,  and  although  I  hold,  for  instance,  the  distinction  between  sensation- 
impulses  and  perception-impulses  to  be  quite  superfluous. — An  important 
alteration  of  our  views  on  heredity  may  perhaps  be  expected  from  Weis- 
mann's  work,  Ueher  die  Vererbung,  Jena,  1883  (English  -translation.  Essays  on 
Heredity  and  Kindred  Biological  Problems,  Oxford:  The  Clarendon  Press, 
1889).    Weismann  regards  the  inheritance  of  traits  acquired  by  use  as  highly 


CHIEF  POINTS  OF  VIEW.  39 

its  actual  contributions  to  the  existence  of  the  same, 
may  be  of  great  assistance  in  the  comprehension  of 
this  function.^  Of  course  we  must  not  suppose,  on 
this  account,  as  many  Darwinians  have  done,  that  we 

improbable,  and  finds  in  the  germ-elements  and  in  the  selection  of  the  germ- 
elements  the  most  important  factors.  We  can  scarcely  withhold  our  assent 
to  Weismann's  arguments,  and  certainly  not  refuse  recognition  to  the  almost 
mathematical  precision  and  depth  of  his  presentation  of  the  problem.  But 
that  the  germ-elements  themselves  may  be  altered  by  outer  influences  appears 
to  be  clearly  shown  by  the  formation  of  new  races,  which  maintain  themselves 
as  such,  transmit  their  racial  traits,  and  are  themselves,  again,  capable  of 
alteration,  under  other  circumstances.  Accordingly,  some  influence  must 
certainly  be  exerted  on  the  germ-plasm  by  the  body  which  envelops  it  (as 
Weismann  himself  admits).  Thus  an  influence  of  the  individual  life  upon 
descendants  can  certainly  not  be  entirely  excluded,  even  although  a  direct 
transmission  to  the  descendants  of  the  results  of  use  in  the  individual  is  {ac- 
cording to  Weismann)  not  to  be  expected. 

[I  have  to  add  here  that  I  lay  great  stress  on  the  works  of  C.  Lloyd  Mor- 
gan, with  which  I  have  since  become  acquainted,  and  that  I  agree  in  almost 
every  point  with  his  expositions. — 1895.] 

ISuch  teleological  conceptions  have  often  been  useful  and  instructive  to 
me.  The  remark,  for  example,  that  a  visible  object  imder  varying  intensity 
of  illumination  can  be  recognised  as  the  same  only  when  the  sensation  ex- 
cited is  in  dependence  on  the  ratio  of  the  illumination-intensities  of  object 
and  surroundings,  makes  intelligible  a  whole  train  of  organic  properties  of 
the  eye.  We  understand  through  it,  also,  how  the  organism,  in  the  interest 
of  its  survival,  was  obliged  to  adjust  itself  to  the  requirement  mentioned  and 
to  adapt  itself  to  feel  the  ratios  of  light-intensity.  The  so-called  law  of  We- 
ber, or  the  fundamental  psycho-physical  formula  of  Fechner,  thus  appears 
not  as  something  fundamental,  but  as  the  explicable  result  of  organic  adjust- 
ments. The  belief  in  the  universal  validity  of  this  law  is,  naturally,  herewith 
relinquished.  I  have  given  the  arguments  on  this  point  in  various  papers. 
{Sitzungsberichte  der  Wiener  Akademie,  Vol.  LII.,  1865 ;  Vierteljakrsschrift 
fUr  Psychiatrie,  Neuwied  and  Leipsic,  1868 ;  Sitzungsberichte  der  Wiener  Aka- 
demie, Vol.  LVII.,  1868).  In  the  last-named  paper,  proceeding  from  the  pos- 
tulate of  the  parallelism  between  the  psychical  and  the  physical,  or,  as  I  then 
expressed  myself,  from  \}a.& proportionality  between  excitation  and  sensation, 
I  abandoned  the  metrical  formula  of  Fechner  (the  logarithmic  law),  and 
brought  forward  another  conception  of  the  fundamental  formula,  the  validity 
of  which  for  light-sensation  I  never  disputed.  This  is  apparent  beyond  all 
doubt  from  the  mathematical  development  there  found.  Thus  one  cannot 
say,  as  Hering  has  done,  that  I  everywhere  take  the  psycho-physical  law  as 
my  foundation,  if  by  this  is  understood  the  metrical  forinula.  How  could  I 
maintain  the  proportioitality  between  excitation  and  sensation  at  the  same 
time  with  the  logarithmic  dependence?  It  was  sufficient  for  me  to  render  my 
meaning  clear; — to  criticise  and  contest  Fechner's  Jaw  in  detail,  I  had,  for 
many  obvious  reasons,  no  need. 


40 


THE  ANALYSIS  OF  THE  SENSATIONS. 


have  *' mechanically  explained"  a  function,  when  we 
discover  that  it  is  necessary  for  the  survival  of  the 
species.  Darwin  himself  is  doubtless  quite  free  from 
this  short-sighted  conception.  The  physical  means  by 
which  a  function  is  developed  still  remains  a  physical 
problem  ;  while  the  mode  and  reason  of  an  organism's 
voluntary  adaptation  continues  to  be  a  psychological 
problem.  The  preservation  of  the  species  is  only 
one,  though  an  actual  and  very  valuable,  point  of  de- 
parture for  inquiry,  but  it  is  by  no  means  the  last  and 
the  highest.  Species  have  certainly  been  destroyed, 
and  new  ones  have  as  certainly  arisen.  The  pleasure- 
seeking  and  pain-avoiding  will,  therefore,  is  directed 
perforce  beyond  the  preservation  of  the  species.  It 
preserves  the  species  when  it  is  advantageous  to  do  so ; 
transforms  it  when  it  is  advantageous  ;  and  destroys 
it  when  its  continuance  would  not  be  advantageous. 
Were  it  directed  merely  to  the  preservation  of  the  spe- 
cies, it  would  move  aimlessly  about  in  a  vicious  circle, 
deceiving  both  itself  and  all  individuals.  This  would 
be  the  biological  counterpart  of  the  notorious  *' per- 
petual motion  "  of  physics.^ 

1  [The  same  absurdity  is  committed  by  the  statesman  who  regards  the  in- 
dividual as  existing  solely  for  the  sake  of  the  State.— 1895.] 


THE  SPACE-SENSATIONS  OF  THE 
EYE. 


I. 


THE  tree  with  its  hard,  rough,  grey  trunk,  its  num- 
berless branches  swayed  by  the  wind,  its  smooth 
soft,  shining  leaves,  appears  to  us  at  first  a  single,  in- 
divisible whole.  In  like  manner,  we  regard  the  sweet, 
round,  yellow  fruit,  the  warm,  bright  fire,  with  its 
manifold  moving  tongues,  as  a  single  thing.  One  name 
designates  the  whole,  one  word  draws  forth  from  the 
depths  of  oblivion  all  associated  memories,  as  if  they 
were  strung  upon  a  single  thread. 

The  reflexion  of  the  tree,  the  fruit,  or  the  fire  in  a 
mirror  is  visible,  but  not  tangible.  When  we  turn  our 
glance  away  or  close  our  eyes,  we  can  touch  the  tree, 
taste  the  fruit,  feel  the  fire,  but  we  cannot  see  them. 
Thus  the  apparently  indivisible  thing  is  separated  into 
parts,  which  are  not  only  connected  with  one  another 
but  are  also  joined  to  other  conditions.  The  visible 
is  separable  from  the  tangible,  from  that  which  may 
be  tasted,  etc. 

The  visible  also  appears  at  first  sight  to  be  a  single 


42  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

thing.  But  we  may  see  a  round,  yellow  fruit  together 
with  a  yellow,  star-shaped  blossom.  A  second  fruit  is 
just  as  round  as  the  first,  but  is  green  or  red.  Two 
things  may  be  alike  in  color  but  unlike  in  form  ;  they 
may  be  different  in  color  but  like  in  form.  Thus  sen- 
sations of  sight  are  separable  into  color-sensations  and 
space-sensations. 


Color-sensation,  into  the  details  of  which  we  shall 
not  enter  here,  is  essentially  a  sensation  of  favorable 
or  unfavorable  chemical  conditions  of  life.  In  the  pro- 
cess of  adaptation  to  these  conditions,  color-sensation 
may  have  been  developed  and  modified.^     Light  in- 

ICompare  Grant  Allen,  The  Caior-Sense  (London:  TrQbner  &  Co.,  1879). 
The  attempt  of  H.  Magnus  to  show  a  considerable  development  of  the  color- 
sense  within  historical  times,  cannot,  I  think,  be  regarded  as  a  felicitous  one. 
Immediately  after  the  appearance  of  the  writings  of  Magnus,  I  corresponded 
with  a  philologist.  Prof.  F.  Polle  of  Dresden,  on  this  subject,  and  both  of  us 
soon  came  to  the  conclusion  that  the  views  of  Magnus  could  not  hold  their 
own  before  the  critical  examination  either  of  natural  science  or  of  philology 
As  each  of  us  left  the  publication  of  the  results  of  our  discussion  to  the  other 
these  were  never  made  public.  Meantime,  however,  the  matter  was  disposed  of 
by  E.  Krause,  and  notably  by  A.  Marty.  I  shall  take  the  liberty  of  adding  only 
a  few  brief  remarks.  From  defects  of  terminology  we  cannot  infer  the  absence 
of  corresponding  qualities  of  sensation.  Terms,  even  to-day,  are  always  indis 
tinct,  hazy,  defective,  and  few  in  number,  where  there  is  no  necessity  for 
sharp  discrimination.  The  color-terminology  of  the  countrjrman  of  to-day- 
and  his  terminology  of  sensations  in  general,  is  no  more  developed  than  that 
of  the  Greek  poets.  The  peasants  of  Marchfeld  say,  for  example,  as  I  have 
often  proved  by  personal  experience,  that  salt  is  "sour,"  because  the  expres- 
sion "salty  "  is  not  familiar  to  them.  The  terminology  of  colors  must  not  be 
looked  for  in  the  poets,  but  in  technical  works.  And,  furthermore,  as  my  col- 
league Benndorf  has  remarked,  we  must  not  take  an  enumeration  of  vase- 
pigments  for  an  enumeration  of  all  colors,  as  does  Mr.  Magnus.  When  we 
consider  the  polychromy  of  the  ancient  Egyptians  and  Pompeiians,  when  we 
take  into  account  the  fact  that  these  decorations  can  scarcely  have  been  pro- 
duced by  the  color-blind,  when  we  note  that  Pompeii  was  buried  in  ashes  only 
seventy  years  after  Virgil's  death,  whilst  Virgil  on  this  theory  is  supposed  to 
have  been  nearly  color-blind,  the  untenability  of  the  whole  conception  is 


THE  SPACE-SENSATIONS  OF  THE  EYE.  43 

troduces  organic  life.  The  green  chlorophyll  and  the 
(complementary)  red  haemoglobin  play  a  prominent 
part  in  the  chemical  processes  of  the  plant-body  and 
in  the  contrary  processes  of  the  animal  body.  The  two 
substances  present  themselves  to  us  in  the  most  varied 
modifications  of  tint.  The  discovery  of  the  visual 
purple,  observations  in  photography  and  photochem- 
istry render  the  conception  of  processes  of  sight  as 
chemical  processes  permissible.  The  role  which  color 
plays  in  analytical  chemistry,  in  spectrum-analysis,  in 
crystallography,  is  well  known.  It  suggests  a  new  con- 
ception for  the  so-called  vibrations  of  light,  according 
to  which  they  are  regarded,  not  as  mechanical,  but  as 
chemical  vibrations,  as  successive  union  and  separa- 
tion, as  an  oscillatory  process  of  the  same  sort  that  takes 
place,  though  only  in  one  direction,  in  photo-chemical 
phenomena.  This  conception,  which  is  substantially 
supported  by  recent  investigations  in  abnormal  dis- 
persion, accords  with  the  electro-magnetic  theory  of 
light.  In  the  case  of  electrolysis,  in  fact,  chemistry 
yields  the  most  intelligible  conception  of  the  electric 


strikingly  apparent.  Applications  of  the  Darwinian  theory  are  also  to  be 
made  with  caution  in  another  direction.  We  like  to  picture  to  ourselves  a 
condition  in  which  the  color-sense  is  lacking,  or  in  which  little  color-sense 
exists,  as  preceding  another  in  which  the  color-sense  is  highly  developed.  For 
the  beginner  it  is  natural  to  proceed  from  the  simple  to  the  complex.  But 
this  is  not  necessarily  the  path  of  Nature.  The  color-sense  exists,  and  it 
is  probably  variable.  But  whether  it  is  being  enriched  or  impoverished — who 
can  tell?  Is  it  not  possible  that,  with  the  awakening  of  intelligence  and  the 
use  of  artificial  contrivance,  the  whole  development  will  be  devolved  on  the 
intellect, — which  certainly  is  chiefly  called  in  play  from  this  point  on, — and 
that  the  development  of  the  lower  organs  of  man  will  be  relegated  to  second 
place? 


44  THE  ANALYSIS  OF  THE  SENSATIONS. 

current,  regarding  the  two  components  of  the  electro- 
lyte as  passing  through  each  other  in  opposite  direc- 
tions. It  is  likely,  therefore,  that  in  a  future  theory 
of  colors,  many  biologico-psychological  and  chemico- 
physical  threads  will  be  united. 


Adaptation  to  the  chemical  conditions  of  life  which 
manifest  themselves  in  color,  renders  locomotion  neces- 
sary to  a  far  greater  extent  than  adaptation  to  those 
which  manifest  themselves  through  taste  and  smell. 
At  least  this  is  so  in  the  case  of  man,  concerning  whom 
alone  we  are  able  to  judge  with  immediacy  and  cer- 
tainty. The  close  association  of  space-sensation  (a 
mechanical  factor)  with  color-sensation  (a  chemical 
factor)  is  herewith  rendered  intelligible.  We  shall  now 
proceed  to  the  analysis  of  space-sensations. 


In  examining  two  figures  which  are  alike  but  dif- 
ferently colored  (for  example,  two  letters  of  the  same 
size  and  shape,  but  of  different  colors), 

NMBIj     we  recognise  their  sameness  of  form  at 
B|^      the  first  glance,  in  spite  of  the  differ- 

■^^     ence  of  color-sensation.     The  sight-per- 

ceptions,  therefore,  must  contam  some 
like  sensation-components.  These  are  the  space-sen- 
sations— which  are  the  same  in  the  two  cases. 


THE  SPACE-SENSATIONS  OF  THE  EYE,  45 


We  will  now  investigate  the  character  of  the  space- 
sensations  that  physiologically  condition  the  recogni- 
tion of  a  figure.  First,  it  is  clear  that  this  recognition 
is  not  the  result  of  geometrical  considerations — which 
are  a  matter,  not  of  sensation,  but  of  intellect.  On  the 
contrary,  the  space-sensations  fn  question  serve  as  the 
starting-point  and  foundation  of  all  geometry.  Two 
figures  may  be  geometrically  congruent,  but  physio- 
logically quite  different,  as  is  shown  by  the  two  ad- 


Fig.  3. 
joined  squares  (Fig.  3),  which  could  never  be  recog- 
nised as  the  same  without  mechanical  and  intellectual 
operations.^     A  few  simple  experiments  will 
render  us  familiar  with  the  relations  here  in- 
volved.    Look  at  the  spot  in  Fig.  4.     Place 
the  same  spot  twice  or  several  times  in  ex-       ^*^-  *• 
actly  the  same  position  in  a  row  (Fig.  5)  ;  the  result 
is  a  peculiar,  agreeable  impression,  and  we  recognise 

1  Compare  my  brief  paper,  Ueber  das  Sehen  von  Lagen  unci  Winkeln,  in  the 
Sitzungsberichte  der  Wiener  Akademie,  Vol.  XLIII.,  1861,  p.  215. 


I 


46  THE  ANALYSIS  OF  THE  SENSATIONS. 

mill 

Fig.  5. 

at  once  and  without  difficulty  the  identity  of  all  the 

figures.     Turning,  however,  one  spot  half  way  around 

with  respect  to  the  other  (Fig.  6),  their 

identity  of  form    is  not  recognisable 

without    intellectual   assistance.      On 

Fig.  6.  ^]^g  other  hand,  if  we  place  two  of  the 

M^  spots  in  positions  symmetrical  to  the 

^F^^L         median  plane  of  the  observer  (Fig.  7), 

^^^  ^^      the  relationship  of  form  is  strikingly 

pig  7 

apparent.   But  if  the  plane  of  symme- 
try diverges  considerably  from   the  median  plane  of 
the  observer,  as  in  Fig.  8,  the  affinity  of  form  is  rec- 
ognisable  only  by  turning  the  figure  around 
^P       or  by  an  intellectual  act.     On  the  other  hand, 
4^       the  affinity  of  form  is  again  apparent  on  con- 
^^v        trasting  with  such  a  spot  the  same  spot  ro- 
^^       tated  through  an  angle  of  180°  in  the  same 
Fig.  8.       plane  (Fig.  9).     In  this  case  we  have  the  so- 

j^      called  centric  symmetry. 
^^K  If  we  reduce  all  the  dimensions  of  the  spot 

r^^^       proportionately,  we  obtain   a  geometrically 
similar  spot.     But  as  the  geometrically  con- 
gruent is  not  necessarily  physiologically  (op- 
^^^'^'        tically)    congruent,    nor    the    geometrically 
symmetrical  necessarily  optically  symmetrical,  analo- 
gously the  geometrically  similar  is  not  necessarily  op- 


Fig.  10.  Fig.  II. 

4Cv  Ir 


THE  SPACE-SENSATIONS  OF  THE  EYE.  47 

tically  similar.  If  the  geometrically  similar  spots  be 
placed  beside  each  other  in  the  saine  relative  positions 
(Fig.  10),  the  two  will  also  appear  optically  similar. 
Turning  one  of  the  spots  around  destroys  the  resem- 
blance (Fig.  1 1).  If  we  sub- 
stitute for  one  of  the  spots 
a  spot  symmetrical  to  the 

other  in  respect  to  the  me-  ^^e-  ^°-  ^^e.  "• 

dian  plane  of  the  observer 
(Fig.  12),  a  symmetrical 
similarity  will  be  produced 
which  has  also  an  optical  ^^' "  ^^'  ^^' 

value.  The  turning  of  one  of  the  figures  through  180° 
in  its  own  plane,  producing  thereby  centrically  sym- 
metrical similarity,  has  also  a  physiologico-optical 
value  (Fig.  13). 

6. 

In  what,  now,  does  the  essential  nature  of  optical 
similarity,  as  contrasted  with  geometrical  similarity, 
consist?  In  geometrically  similar  figures,  all  homolo- 
gous distances  are  proportional.  But  this  is  an  affair 
of  the  intellect,  not  of  sensation.  If  we  place  beside  a 
triangle  with  the  sides  ^,  b,  c,  a  triangle  with  the  sides 
2«,  2by  2Cf  we  do  not  recognise  the  simple  relation  of 
the  two  immediately,  but  intellectually,  by  measure- 
ment. If  the  similarity  is  to  become  optically  percep- 
tible, the  proper  position  must  be  added.  That  a 
simple  intellectual  relationship  of  two  objects  does  not 


48  THE  ANALYSIS  OF  THE  SENSATIONS. 

necessarily  condition  a  similarity  of  sensation,  may  be 
perceived  by  comparing  two  triangles  having  respec- 
tively the  sides  a,  b,  c,  and  a-^-m^  b-\-tn,  c-\-m.  The 
two  triangles  do  not  look  at  all  alike.  Similarly  all 
conic  sections  do  not  look  alike,  although  all  stand  in 
a  simple  geometric  relation  to  each  other  ;  still  less  do 
curves  of  the  third  order  exhibit  optical  similarity;  etc. 


The  geometrical  similarity  of  two  figures  is  deter- 
mined by  all  their  homologous  lines  being  proportional 
or  by  all  their  homologous  angles  being  equal.     But 

to  appear  optically  simi- 
lar the  figures  must  also 
be  similarly  situated^  that 
is  all  their  homologous 

Fig.  14. 

lines  must  be  parallel  or. 


e£^L 


as  we  prefer  to  say,  have  the  same  direction  (Fig.  14). 
The  importance  of  direction  for  sensation  will  be  evi- 
dent upon  a  careful  consideration  of  Fig.  3.  By  like 
ness  of  direction,  accordingly,  are  determined  like 
space-sensations,  and  these  are  characteristic  of  the 
physiologico-optical  similarity  of  figures.^ 

1  Some  twenty  years  ago,  in  a  society  of  physicists  and  physiologists,  I 
proposed  for  discussion  the  question,  why  geometrically  similar  figures  were 
also  optically  similar.  I  remember  quite  well  the  attitude  taken  with  regard 
to  this  question,  which  was  accounted  not  only  superfluous,  but  even  ludi- 
crous. Nevertheless,  I  am  now  as  strongly  convinced  as  I  was  then  that  the 
question  involves  the  whole  problem  of  form-vision.  That  a  problem  cannot 
be  solved  which  is  not  recognised  as  such  is  clear.  In  this  non-recognition, 
however,  is  manifested,  in  my  opinion,  that  one-sided  mathematicophysical 
direction  of  thought,  which  alone  accounts  for  the  opposition,  instead  of 
cheerful  acceptance,  with  which  the  writings  of  tiering  have  been  received. 


THE  SPACE-SENSATIONS  OF  THE  EYE. 


49 


We  may  obtain  an  idea  of  the  physiological  sig- 
nificance of  the  direction  of  a  given  straight  line  or 
curve-element,  by  the  following  reflexion.  Let  y  =f(x) 
be  the  equation  of  a  plane  curve.  We  can  read  at  a 
glance  the  course  of  the  values  of  dyjdx  on  the  curve, 
for  they  are  determined  by  its  slope  ;  and  the  eye  gives 
us,  likewise,  qualitative  information  concerning  the 
values  of  d'^y/dx'^,  for  they  are  characterised  by  the 
curvature.  The  question  naturally  presents  itself  why 
can  we  not  arrive  at  as  immediate  conclusions  con- 
cerning the  values  d^y/dx^,  d^yjdx^y  etc.  The  an- 
swer is  easy.  What  we  see  are  not  the  differential 
coefficients,  which  are  an  intellectual  affair,  but  only 
the  direction  of  the  curve-elements,  and  the  declination 
of  the  direction  of  one  curve-element  from  that  of  an- 
other. 

In  fine,  since  we  are  immediately  cognisant  of  the 
similarity  of  figures  lying  in  similar  positions,  and  are 
also  able  to  distinguish  without  ado  the  special  case  of 
congruity,  therefore  our  space-sensations  yield  us  in- 
formation concerning  likeness  or  unlikeness  of  directions 
and  equality  or  inequality  of  spatial  dimensions. 

8. 

It  is  extremely  probable  that  sensations  of  space 
are  produced  by  the  motor  apparatus  of  the  eye.  With- 
out entering  into  particulars,  we  may  observe,  first, 
that  the  whole  apparatus  of  the  eye,  and  especially 
the  motor  apparatus,  is  symmetrical  with  respect  to 


50  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

the  median  plane  of  the  head.  Hence,  symmetrical 
movements  of  looking  will  determine  like  or  approxi- 
mately like  space-sensations.  Children  constantly  con- 
found the  letters  b  and  d^  as  also  /  and  q.  Adults, 
too,  do  not  readily  notice  a  change  from  left  to  right 
unless  some  special  points  of  apprehension  for  sense 
or  intellect  render  it  perceptible.  The  symmetry  of 
the  motor  apparatus  of  the  eye  is  very  perfect.  The 
like  excitation  of  its  symmetrical  organs  would,  by  it- 
self, scarcely  account  for  the  distinction  of  right  and 
left.  But  the  whole  human  body,  especially  the  brain, 
is  affected  with  a  slight  asymmetry, — which  leads,  for 
example,  to  the  preference  of  one  (generally  the  right) 
hand,  in  motor  functions.  And  this  leads,  again,  to  a 
further  and  better  development  of  the  motor  functions 
of  the  right  side,  and  to  a  modification  of  the  attend- 
ant sensations.  After  the  space-sensations  of  the  eye 
have  become  associated,  through  writing,  with  the  mo- 
tor functions  of  the  right  hand,  a  confusion  of  those 
vertically  symmetrical  figures  with  which  the  art  and 
habit  of  writing  are  concerned  no  longer  ensues.  This 
association  may,  indeed,  become  so  strong  that  re- 
membrance follows  only  the  accustomed  tracks,  and 
we  read,  for  example,  the  reflexion  of  written  or  printed 
words  in  a  mirror  only  with  the  greatest  difficulty. 
The  confusion  of  right  and  left  still  occurs,  however, 
with  regard  to  figures  which  have  no  motor,  but  only 
a  purely  optical  (for  example,  ornamental)  interest. 
A  noticeable  difference  between  right  and  left  must  be 


THE  SPACE-SENSATIONS  OF  THE  EYE.  51 

felt,  moreover,  by  animals,  as  in  many  predicaments 
they  have  no  other  means  of  finding  their  way.  The 
similarity  of  sensations  connected  with  symmetrical 
motor  functions  is  easily  remarked  by  the  attentive 
observer.  If,  for  example,  supposing  my  right  hand 
to  be  employed,  I  grasp  a  micrometer-screw  or  a  key 
with  my  left  hand,  I  am  certain  (unless  I  reflect  be- 
forehand) to  turn  it  in  the  wrong  direction, — that  is,  I 
always  perform  the  movement  which  is  symmetrical 
to  the  usual  movement,  confusing  the  two  because  of 
the  similarity  of  the  sensation.  The  observations  of 
Heidenhain  regarding  the  reflected  writing  of  persons 
hypnotised  on  one  side  should  also  be  cited  in  this 
connexion. 

With  looking  upwards  and  looking  downwards, 
fundamentally  different  space-sensations  are  asso- 
ciated, as  ordinary  observation  will  show.  This  is, 
moreover,  comprehensible,  since  the  motor  apparatus 
of  the  eye  is  asymmetrical  with  respect  to  a  horizontal 
plane.  The  direction  of  gravity  is  so  very  decisive 
and  important  for  the  motor  apparatus  of  the  rest  of 
the  body  that  the  same  factor  has  assuredly  also  found 
its  expression  in  the  apparatus  of  the  eye,  which  serves 
the  rest.  It  is  well  known  that  the  symmetry  of  a 
landscape  and  of  its  reflexion  in  water  is  not  felt. 
The  portrait  of  a  familiar  personage,  when  turned  up- 
side down,  is  strange  and  puzzling  to  a  person  who 
does  not  recognise  it  intellectually.  If  we  place  our- 
selves behind  the  head  of  a  person  lying  upon  a  couch 


52  THE  ANALYSIS  OF  THE  SENSATIONS. 

and  unreflectingly  give  ourselves  up  to  the  impression 
which  the  face  makes  upon  us,  we  shall  find  that  it  is 
altogether  strange,  especially  when  the  person  speaks. 
The  letters  b  and  /,  and  d  and  ^,  are  not  confused  by 
children. 

Our  previous  remarks  concerning  symmetry,  simi- 
larity, and  the  rest,  naturally  apply  not  only  to  plane 
figures,  but  also  to  those  in  space.  Hence,  we  have 
yet  a  remark  to  add  concerning  the  sensation  of  space- 
depth.  Looking  at  objects  afar  off  and  looking  at 
objects  near  at  hand  determine  different  sensations. 
These  sensations  viust  not  be  confused,  because  of  the 
supreme  importance  of  the  difference  between  near 
and  far,  both  for  animals  and  human  beings.  They 
cannot  be  confused  because  the  motor  apparatus  is 
asymmetrical  with  respect  to  a  plane  perpendicular  to 
the  direction  from  front  to  rear.  The  observation  that 
the  bust  of  a  familiar  personage  cannot  be  replaced  by 
the  mould  in  which  the  bust  is  cast  is  quite  analogous 
to  the  observations  consequent  upon  the  inversion  of 
objects. 


If  equal  distances  and  like  directions  excite  like 
space-sensations,  and  directions  symmetrical  with  re- 
spect to  the  median  plane  of  the  head  excite  similar 
space-sensations,  the  explanation  of  the  above-cited 
facts  is  not  far  to  seek.  The  straight  line  has,  in  all 
its  elements,  the  same  direction,  and  everywhere  ex- 


THE  SPACE-SENSATIONS  OF  THE  EYE.  53 

cites  the  same  space-sensations.  Herein  consists  its 
aesthetic  value.  Moreover,  straight  lines  which  lie  in 
the  median  plane  or  are  perpendicular  to  it  are  brought 
into  special  relief  by  the  circumstance  that,  through 
this  position  of  symmetry,  they  occupy  a  like  position 
to  the  two  halves  of  the  visual  apparatus.  Every  other 
position  of  the  straight  line  is  felt  as  awryness,  or  as 
a  deviation  from  the  position  of  symmetry. 

The  repetition  of  the  same  space-figure  in  the  same 
position  conditions  a  repetition  of  the  same  space-sen- 
sation. All  lines  connecting  prominent  (noticeable) 
homologous  points  have  the  same  direction  and  excite 
the  same  sensation.  Likewise  when  merely  geometri- 
cally similar  figures  are  placed  side  by  side  in  the  same 
positions,  this  relation  holds.  The  sameness  of  the 
dimensions  alone  is  absent.  But  when  the  positions 
are  disturbed,  this  relation,  and  with  it,  the  impression 
of  unity — the  aesthetic  impression — are  also  disturbed. 

In  a  figure  symmetrical  with  respect  to  the  median 
plane,  similar  space-sensations  corresponding  to  the 
symmetrical  directions  take  the  place  of  the  identical 
space-sensations.  The  right  half  of  the  figure  stands 
in  the  same  relation  to  the  right  half  of  the  visual  ap- 
paratus as  the  left  half  of  the  figure  does  to  the  left 
half  of  the  visual  apparatus.  If  we  alter  the  sameness 
of  the  dimensions,  the  sensation  of  symmetrical  simi- 
larity is  still  felt.  An  oblique  position  of  the  plane  of 
symmetry  disturbs  the  whole  effect. 

If  we  turn   a  figure  through   180'',  contrasting  it 


54  THE  ANALYSIS  OF  THE  SENSATIONS. 

with  itself  in  its  original  position,  centric  symmetry  is 
produced.  That  is,  if  two  pairs  of  homologous  points 
be  connected,  the  connecting  lines  will  cut  each  other 
at  a  point  6>,  through  which,  as  their  point  of  bisec- 
tion, all  lines  connecting  homologous  points  will  pass. 
Moreover,  in  the  case  of  centric  symmetry,  all  lines  of 
connexion  between  homologous  points  have  the  same 
direction, — a  fact  which  produces  an  agreeable  sensa- 
tion. If  the  sameness  of  the  dimensions  is  eliminated, 
there  still  remains,  for  sensation,  centrically  symmetri- 
cal similarity. 

Regularity  appears  to  have  no  special  physiological 
value,  in  distinction  from  symmetry.  The  value  of 
regularity  probably  lies  rather  in  its  manifold  syvnTnetry, 
which  is  perceptible  in  more  than  one  single  position. 

lO. 

The  correctness  of  these  observations  will  be  ap- 
parent on  glancing  over  the  work  of  Owen  Jones — A 
Grammar  of  Ornanient  (London,  1865).  In  almost 
every  plate  one  finds  new  and  different  kinds  of  sym- 
metry as  fresh  testimony  in  favor  of  the  conceptions 
above  advanced.  The  art  of  decoration,  which,  like 
pure  instrumental  music,  aims  at  no  ulterior  end,  but 
ministers  only  to  pleasure  in  form  (and  color),  is  the 
best  source  of  material  for  our  present  studies.  Writ- 
ing is  governed  by  other  considerations  than  that  of 
beauty.  Nevertheless,  we  find  among  the  twenty-four 
large  Latin  letters  ten  which  are  vertically  symmetri- 


THE  SPACE-SENSATIONS  OF  THE  EYE.  55 

cal  (A,  H,  I,  M,  O,  T,  V,  W,  X,  Y),  five  which  are 
horizontally  symmetrical  (B,  C,  D,  E,  K),  three  which 
are  centrically  symmetrical  (N,  S,  Z),  and  only  six 
which  are  unsymmetrical  (F,  G,  L,  P,  Q,  R). 

II. 

It  is  to  be  remarked  again  that  the  geometrical 
and  the  physiological  properties  of  a  figure  in  space 
are  to  be  sharply  distinguished.  The  physiological 
properties  are  determined  by  the  geometrical  proper- 
ties coincidently  with  these,  but  are  not  determined 
by  these  solely.  On  the  other  hand,  physiological 
properties  very  probably  gave  the  first  impulse  to 
geometrical  investigations.  The  straight  line  doubt- 
less attracted  attention  not  because  of  its  being  the 
shortest  line  between  two  points,  but  because  of 
its  physiological  simplicity.  The  plane  likewise  pos- 
sesses, in  addition  to  its  geometrical  properties,  a  spe- 
cial physiologico- optical  (aesthetic)  value,  which  claims 
notice  for  it,  as  will  be  shown  later  on.  The  division 
of  the  plane  and  of  space  by  right  angles  has  not  only 
the  advantage  of  producing  equal  parts,  but  also  an 
additional  and  special  symmetry-value.  The  circum- 
stance that  congruent  and  similar  geometrical  figures 
can  be  brought  into  positions  where  their  relationship 
is  physiologically  felt,  led,  no  doubt,  to  an  earlier 
investigation  of  these  kinds  of  geometrical  relation- 
ship than  of  those  that  are  less  noticeable,  such  as  af- 
finity, collineation,  and  others.     Without  the  co-ope- 


56  THE  ANALYSIS  OF  THE  SENSATIONS. 

ration  of  sense-perception  and  understanding,  a  scien- 
tific geometry  is  inconceivable.  But  H.  Hankel  has 
admirably  shown  in  his  History  of  Matheftiatics  (Leip- 
sic,  1874)  that  in  the  Greek  geometry  the  factor  of 
pure  understanding,  in  the  Indian,  on  the  other  hand, 
that  of  sense,  very  considerably  predominated.  The 
Hindus  make  use  of  the  principles  of  symmetry  and 
similarity  (see,  for  example,  p.  206  of  HankePs  book) 
with  a  generality  which  is  totally  foreign  to  the  Greeks. 
Hankel's  proposition  to  unite  the  rigor  of  the  Greek 
method  with  the  perspicuity  of  the  Indian  in  a  new 
mode  of  presentation  is  well  worthy  consideration. 
Furthermore,  in  so  doing,  we  should  only  be  following 
in  the  footsteps  of  Newton  and  John  Bernoulli,  who 
have  made  a  still  more  general  application  of  the  prin- 
ciple of  similitude  in  mechanics.  The  advantages  that 
the  principle  of  symmetry  affords  in  the  last-named 
province,  I  have  shown  elsewhere.^ 

1 1  have  given  less  complete  discussions  of  the  leading  thoughts  of  this 
chapter  in  the  paper  already  mentioned,  Ueber  das  Sehen  von  Lagen  und  Win- 
keln  (1861),  further  in  Y\c)\\.€ %  ZeitschriftfUr  Philosophie,  Vol.  XLVI.,  1865,  p.  5 
and  in  The  Forms  of  Liquids,  and  Symmetry  (1872)  now  also  published  in  my 
Popular  Scientific  Lectures,  translated  by  Thomas  J.  McCormack,  Open  Court 
Publishing  Co.,  Chicago,  1894.  With  regard  to  the  use  of  the  principle  of 
symmetry  in  mechanics,  compare  my  work  The  Science  of  Mechanics  (1883), 
translated  by  Thomas  J,  McCormack,  1893,  Open  Court  Pub.  Co.,  Chicago, 
[I  must  also  refer  in  this  place  to  a  work  which  has  since  appeared,  by  J.  L. 
Soret,  Des  conditions  physiques  de  la  perception  du  beau,  Geneva,  1892.  In  this 
charmingly  written  book  Soret  makes  extensive  applications  of  the  principle 
of  repetition  of  sensations  to  aesthetics.  Applications  of  this  kind  I  had  treated 
only  briefly,  as  it  was  not  my  purpose  to  write  a  book  on  aesthetics.  On  the 
other  hand,  I  believe  I  have  penetrated  deeper  into  the  physiological  and 
psychological  aspect  of  the  principle.— Mach,  1895.] 


INVESTIGATION  OF  SPACE-SENSA- 
TION CONTINUED.* 


That  space-sensation  is  connected  with  motor  pro- 
cesses has  long  since  ceased  to  be  disputed.  Opinions 
differ  only  as  to  how  this  connexion  is  to  be  repre- 
sented. 


If  two  congruent  images  of  different  colors  fall  in 
succession  on  the  same  parts  of  the  retina,  they  are 
at  once  recognised  as  identical  figures.  We  may, 
therefore,  regard  different  space-sensations  as  con- 
nected with  different  parts  of  the  retina.  But  that 
these  space-sensations  are  not  unalterably  restricted  to 
particular  parts  of  the  retina,  we  perceive  on  moving 

ITo  my  knowledge,  the  matter  treated  in  the  preceding  chapter  has  not  yet 
been  discussed,  except  in  three  small  works  of  my  own.  The  considerations 
of  the  present  chapter,  moreover,  are,  for  me,  founded  upon  those  of  the  pre- 
ceding chapter.  I  indicate  here  the  methods  by  which  I  have  myself  gotten 
clear  regarding  the  sensation  of  space,  without  laying  the  least  claim  to  that 
which  has  been  accomplished  by  others  in  this  direction,  particularly  by  the 
theory  of  Hering.  The  extensive  literature  of  this  subject  is,  moreover,  too 
imperfectly  known  to  me  to  give  exact  references  on  all  points.  The  point  of 
Hering's  theory  which  I  regard  as  the  most  important  I  will  especially  notice. 


58  THE  ANALYSIS  OF  THE  SENSATIONS. 

our  eyes  freely  and  voluntarily,  whereby  the  objects 
observed  do  not  change  their  position  or  form,  although 
their  images  are  displaced  on  the  retina. 

If  I  look  straight  before  me,  fixing  my  eyes  upon 
an  object  (9,  an  object  A,  which  is  reflected  on  the 
retina  in  a,  at  a  certain  distance  below  the  point  of 
most  distinct  vision,  appears  to  me  to  be  situated  at  a 
certain  height.  If  I  now  raise  my  eyes,  fixing  them 
upon  B,  A  retains  its  former  height.  It  would  neces- 
sarily appear  lower  down  if  the 
position  of  the  image  on  the 
retina,  or  the  arc  oa,  alone  de- 
termined the  space-sensation.  I 
^*s- 15.  can  raise  my  glance  as  far  as  A 

and  farther  without  a  change  in  this  relation.  Thus, 
the  physiological  process  which  conditions  the  volun- 
tary raising  of  the  eye,  can  entirely  or  partly  take  the 
place  of  the  height-sensation,  is  homogeneous  with  it, 
or,  in  brief,  algebraically  summationable  with  it.  If 
I  turn  my  eyeball  upward  by  a  slight  pressure  of  the 
finger,  the  object  A  actually  appears  to  sink,  propor- 
tionately to  the  shortening  of  the  arc  oa.  The  same 
thing  happens  when,  by  any  other  unconscious  or  in- 
voluntary process — for  example,  through  a  cramp  of 
the  muscles  of  the  eye — the  eyeball  is  turned  upward. 
According  to  an  experience  now  familiar  to  opticians 
for  some  decades  patients  with  paralysis  of  the  rectus 
externus  reach  too*  far  to  the  right  in  attempting  to 
grasp  objects  at  the  right.     Since  they  need  to  exert  a 


SPACE-SENSATIONS  CONTINUED,  59 

stronger  impulse  of  the  will  than  persons  of  sound 
eyes,  In  order  to  fix  their  glance  upon  an  object  to  the 
right,  the  thought  naturally  suggests  itself  that  the 
will  to  look  to  the  right  determines  the  optical  space- 
sensation  *' right."  Some  years  ago,i  I  put  this  ob- 
servation into  the  form  of  an  experiment,  which  every 
one  can  try  for  himself.  Let  the  eyes  be  turned  as  far 
as  possible  towards  the  left  and  two  large  lumps  of 
moderately  hard  putty  firmly  pressed  against  the  right 
side  of  each  eye-ball.  If,  now,  we  attempt  to  glance 
quickly  to  the  right,  we  shall  succeed  only  very  im- 
perfectly, owing  to  the  incompletely  spherical  form 
of  the  eyes,  and  the  objects  will  suffer  a  strong  dis- 
placement to  the  right.  Thus  the  mere  will  to  look  to 
the  right  imparts  to  the  images  at  certain  points  of  the 
retina  a  larger  ^'rightward  value,'*  as  we  may  term  it 
for  brevity.  The  experiment  is,  at  first,  surprising. 
It  will  soon  be  perceived,  however,  that  both  facts — 
viz.,  that  by  voluntarily  turning  the  eyes  to  the  right, 
objects  are  not  displaced,  and  that  by  the  forced,  in- 
voluntary turning  of  the  eyes  to  the  right,  objects  are 
displaced  to  the  left — together  amount  to  the  same 
thing.  My  eye,  which  I  wish  to,  and  cannot,  turn  to 
the  right,  may  be  regarded  as  voluntarily  turned  to  the 
right  and  compulsorily  turned  back  by  an  outer  force. 

1  Shortly  after  finishing  my  Grundlinien  der  Lehre  von  den  Bewegungs- 
em^findungen. 


6o  THE  ANALYSIS  OF  THE  SENSATIONS. 


The  will  to  perform  movements  of  the  eyes,  or  the 
innervation  to  the  act,  is  itself  the  space-sensation. 
This  follows  naturally  from  the  preceding  considera- 
tion.^ If  we  have  a  sensation  of  itching  or  pricking  in  a 
certain  spot,  by  which  our  attention  is  sufficiently  se- 
cured, we  immediately  grasp  at  the  spot  with  the  cor- 
rect amount  of  movement.  In  the  same  manner  we 
turn  our  eyes  with  the  correct  amount  of  exertion  to- 
wards an  object  reflected  on  the  retina,  as  soon  as  this 
exerts  a  sufficient  stimulus  to  draw  our  attention.  By 
virtue  of  organic  apparatus  and  long  exercise  we  hit 
immediately  upon  the  exact  degree  of  innervation 
necessary  to  enable  us  to  fix  our  eyes  upon  an  object 
reflected  on  a  certain  point  of  the  retina.  If  the  eyes 
are  already  turned  towards  the  right,  and  we  begin  to 
give  our  attention  to  an  object  further  to  the  right  or 
the  left,  a  new  innervation  of  the  same  sort  is  algebra- 
ically added  to  that  already  present.  A  disturbance 
of  the  process  arises  only  when  extraneous,  involun- 
tary innervations  or  outward  moving  forces  are  added 
to  the  innervations  determined  by  the  will. 

4- 
Years  ago,  while  occupied  with  the  questions  now 
under  discussion,  I  noticed  a  peculiar  phenomenon, 

II  retain  the  expression  which  was  first  immediately  suggested  to  me, 
with  no  intention  of  forestalling  future  inquiry. 


SPACE-SENSATIONS  CONTINUED.  6i 

which  has  not  yet,  to  my  knowledge,  been  described. 
In  a  very  dark  room  we  fix  our  eyes  upon  a  light  A, 
and  then  suddenly  look  at  a  light  lower  down,  B.  At 
this,  the  light  A  appears  to  make  a  rapid  sweep  A  A' 
(quickly  ended)  upwards.  The  light  B,  of  course, 
does  the  same — but  to  avoid  complications,  this  is  not 
indicated  in  the  diagram.  The  sweep  is,  of  course,  an 
after-image,  which  enters  consciousness  only  on  com- 
pletion, or  shortly  before  completion,  of  the  glance- 
movement,  but — and 
this  is  the  remark- 
able point — with  po- 
sitional values  that 
correspond,  not  to  the 
later,  but  to  the  ear- 
lier innervations  and 
position   of    the   eye.  p.^^g 

Similar      phenomena 

are  often  noticed  in  experiments  with  Holtz's  elec- 
trical machine.  If  the  experimenter  is  surprised  by 
a  spark  during  a  glance  downwards,  the  spark  often 
appears  high  above  the  electrodes.  If  it  yields  a  per- 
manent after-image,  the  latter  appears,  of  course,  be- 
low the  electrodes.  The  preceding  phenomena  an- 
swer to  the  so-called  personal  equation  of  astronomers, 
except  that  they  are  confined  to  the  province  of  sight. 
By  what  organic  apparatus  this  relation  is  determined 
cannot  be  decided  now,  but  it  is  probably  of  some 


62  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

value  in  preventing  confusion  of  position  in  move- 
ments of  the  eyes. 

5- 

For  the  sake  of  simplicity  we  have  hitherto  re- 
garded only  the  eyes  as  in  motion,  and  have  considered 
the  head  (and  the  body  generally)  as  at  rest.  If,  now, 
we  move  the  head  about  without  intentionally  fixing 
the  eyes  upon  any  object,  the  objects  seen  remain 
motionless.  But  at  the  same  time  another  observer 
may  notice  that  the  eyes,  like  frictionless,  inert  masses, 
take  no  part  in  the  turning  movements.  Still  more 
noticeable  is  the  phenomenon  if 
^_^.,::::j''^  we  turn  for  a  considerable  time 
^.^.^^rrr^g  and  with  continuous  motion  about 

B     :b  a  vertical  axis,  in  the  direction 

Fig.  17. 

of  the  hands  of  a  clock  viewed 
from  above.  In  this  case,  as  Breuer  has  observed,  the 
open  or  closed  eyes  turn,  about  ten  times  to  a  full  revo- 
lution of  the  body,  in  the  opposite  direction  to  that  of 
the  clock- hands,  with  a  uniform  motion,  and  as  fre- 
quently back  again  in  the  opposite  direction  by  jerks. 
The  process  is  represented  in  the  diagram  of  Fig.  17. 
On  O  Ty  the  times  are  laid  off  as  abscissas,  the  angles 
described  in  the  direction  of  the  clock-hands  are  laid 
off  as  ordinates  upwards,  and  the  angles  described  in 
the  opposite  direction  as  ordinates  downwards.  The 
curve  OA  corresponds  to  the  rotation  of  the  body, 
OBB  to  the  relative,  and  O  C  C  to  the  absolute,  rota- 


SPACE-SENSATIONS  CONTINUED.  63 

tion  of  the  eyes.  No  one,  on  repeating  the  experi- 
ment, can  avoid  the  conclusion  that  we  are  concerned 
here  with  an  automatic  (unconscious)  movement  of 
the  eyes,  reflexively  excited  by  the  rotation  of  the 
body.  How  this  motion  is  brought  about  remains, 
naturally,  to  be  investigated.  A  simple  conception 
would  be  that  the  excitation,  uniformly  reaching  two 
antagonistic  organs  of  innervation  on  the  turning  of 
the  body,  is  answered  by  one  with  a  uniform  stream  of 
innervation,  while  the  other  gives  its  impulse  of  inner- 
vation only  after  the  lapse  of  a  certain  time,  like  a 
filled  rain-gauge  suddenly  overturning.  For  us  it  suf- 
fices, provisorily,  to  know  that  this  automatic,  uncon- 
scious compensational  movement  of  the  eye  is  actually 
present. 

The  slower  unconscious  compensational  movement 
of  the  eye  (the  jerking  motion  leaving  behind  it  no  op- 
tical impression)  is  thus  the  cause  of  the  retention  of 
position  by  objects  seen  during  the  turning  of  the  body 
— a  thing  which  is  very  important  for  orientation.  If, 
now,  in  turning  our  head,  we  also  voluntarily  turn  the 
eyes  in  the  same  direction,  fixing  them  upon  one  ob- 
ject after  another,  we  must  overcompensate  the  auto- 
matic, involuntary  innervation  by  the  voluntary  inner- 
vation. We  need  the  same  innervation  as  if  the  whole 
angle  turned  through  were  described  by  the  eye  alone. 
In  this  way  is  explained  why,  when  we  turn  about,  the 
whole  optical  space  appears  to  us  a  continuity  and  not 
an  aggregation  of  fields  of  vision  ;  and  why,  at  the 


64  THE  ANALYSIS  OF  THE  SENSATIONS. 

same  time,  the  optical  objects  remain  stationary.  That 
which  we  see  of  our  own  body,  in  turning,  we  see,  for 
obvious  reasons,  optically  in  motion. 

Thus  we  arrive  at  the  practically  valuable  concep- 
tion of  our  body  as  in  motion  in  a  fixed  space.  We 
understand  why  it  is  that,  in  our  numerous  turnings 
and  ramblings  in  the  streets  and  in  buildings,  and  in 
our  passive  turnings  in  a  wagon  or  in  the  cabin  of  a 
ship — yes,  even  in  the  dark — we  do  not  lose  our  sense 
of  direction,  though  it  is  true  that  the  primary  co- 
ordinates from  which  we  started  gradually  sink  un- 
noticed into  unconsciousness,  and  we  soon  begin  to 
reckon  from  new  objects  around  us.  That  peculiar 
state  of  confusion  as  to  locality  in  which  we  some- 
times find  ourselves  on  suddenly  awaking  at  night, 
where  we  look  about  helplessly  for  the  window  or  the 
table,  is  probably  due  to  dreams  of  movement  imme- 
diately preceding  our  awaking. 

Similar  phenomena  to  those  which  manifest  them- 
selves on  the  rotation  of  the  body  make  their  appear- 
ance in  connexion  with  the  movements  of  the  body 
generally.  If  I  move  my  head  or  my  whole  body  side- 
wise,  I  do  not  lose  sight  of  an  object  on  which  my 
eyes  rest.  The  latter  seems  to  continue  motionless, 
while  the  more  distant  objects  undergo  a  movement  in 
the  same  direction  as  that  of  the  body,  the  nearer  an 
opposite,  parallactic  displacement.  The  parallactic 
displacements  to  which  we  are  accustomed  are  per- 
ceived, but  do  not  cause  us  any  disturbance  and  are 


SPACE-SENSATIONS  CONTINUED.  65 

correctly  interpreted.  But  in  the  monocular  inversion 
of  a  Plateau  wire-net,  the  parallactic  displacements, 
which  in  the  present  case  are  unusual  as  regards 
amount  and  direction,  immediately  attract  the  eye, 
and  apparently  present  to  us  a  revolving  object.^ 

6. 

When  I  turn  my  head,  I  not  only  see  that  part  of 
it  turning  which  I  am  able  to  see  (as  will  be  imme- 
diately understood  from  the  foregoing)  but  I  also  feel 
it  turning.  This  is  due  to  the  fact  that  conditions  exist 
in  the  province  of  touch  which  are  quite  analogous  to 
those  in  the  province  of  sight. ^  When  I  reach  out  my 
hand  to  grasp  an  object,  a  sensation  of  touch  is  com- 
bined with  a  sensation  of  innervation.  If  I  look  to- 
wards the  object,  a  luminous  sensation  is  substituted 
for  the  sensation  of  touch.  Even  where  objects  are  not 
touched,  skin-sensations  may  always  be  perceived  when 
the  attention  is  turned  to  them,  and  these,  combined 

1  Compare  my  "  Beobachtungen  aber  monoculare  Stereoscopie  "  [SitzungS' 
berichte  der  Wiener  Akademie,  Vol.  LVIIL,  1868). 

2 The  view  that  the  sense  of  sight  and  the  sense  of  touch  involve,  so  to 
speak,  the  same  space-sense  as  a  common  element,  was  advanced  by  Locke 
and  contested  by  Berkeley.  Diderot  also  [Lettres  sur  les  aveugles)  is  of  opin- 
ion that  the  space-sense  of  the  blind  is  altogether  different  from  that  of  a  per- 
son who  sees.  Compare  on  this  point  the  acute  remarks  of  Dr.  Th.  Loewy 
(Common  Sensibles.  Die  Gemeinideen  des  Gesichts-  und  Tastsinnes  nach  Locke 
und  Berkeley')  with  whose  results,  however,  I  cannot  agree.  The  circumstance 
that  a  man  blind  from  birth  does  not,  after  being  operated  upon,  visually  dis- 
tinguish the  cubes  and  spheres  with  which  he  is  familiar  from  touch  proves  to 
my  mind  nothing  at  all  against  Locke  and  nothing  in  favor  of  Berkeley  and 
Diderot.  Even  persons  who  see  recognise  figures  that  are  turned  upside 
down  only  after  much  practice.  Besides,  if  Locke  were  wrong,  how  could  a 
blind  Saunderson  have  written  a  geometry  intelligible  to  people  gifted  with 
sight.     Let  a  blind  man  attempt  to  write  a  theory  of  color  I 


66  THE  ANALYSIS  OF  THE  SENSATIONS. 

with  changing  innervations,  also  yield  a  conception  of 
our  body  as  in  motion,  which  quite  accords  with  that 
acquired  by  optical  means. 

Thus,  in  active  movements,  the  skin-sensations  are 
delocalised,  as  we  may  briefly  express  it.  In  passive 
movements  of  the  body,  reflex,  unconscious  innerva- 
tions and  movements  of  compensation  make  their  ap- 
pearance. In  turning  round  to  the  right,  for  example, 
my  skin-sensations  are  connected  with  the  same  inner- 
vations as  would  be  combined  with  the  touching  of 
objects  in  turning  to  the  right.  I  feel  myself  turning 
to  the  right.  If  I  am  passively  turned  toward  the 
right,  the  reflex  endeavor  arises  to  compensate  the 
turning.  I  either  actually  remain  standing  and  feel 
myself  at  rest,  or  I  repress  the  motion  toward  the  left. 
But  for  this  I  need  to  exert  the  same  voluntary  inner- 
vation as  for  an  active  turning  to  the  right,  which  has 
also  the  same  sensation  as  its  result. 

7. 
At  the  time  when  my  work  on  the  Sensations  of 
Movement'^  was  written,  I  had  not  yet  attained  to  a 
thoroughly  comprehensive  view  of  the  simple  relation 
here  described.  I  encountered,  consequently,  difficul- 
ties in  the  explanation  of  certain  phenomena,  observed 
by  Breuer  and  myself,  which  are  now  easy  of  explana- 
tion, and  which  I  will  briefly  notice.     If  an  observer 


1  Grundlinien  der  Lehre  -non  den  Bewegungsempfindungen.  Leipsic :  Enge^ 
mann,  1875.    P.  83. 


SPACE-SENSATIONS  CONTINUED.  67 

be  shut  up  in  a  closed  receptacle,  and  the  receptacle 
be  set  in  rotation  toward  the  right,  the  same  will  ap- 
pear to  the  observer  in  rotation,  although  every  ground 
of  inference  for  relative  rotation  is  wanting.  If  his 
eyes  perform  involuntary,  compensatory  movements 
to  the  left,  the  images  on  the  retina  will  be  displaced, 
with  the  result  that  he  has  the  sensation  of  movement 
toward  the  right.  If,  however,  he  fixes  his  eyes  upon 
the  receptacle,  he  must  voluntarily  compensate  the  in- 
voluntary movements,  and  thus  again  he  is  conscious 
of  movement  towards  the  right.  It  is  plain,  there- 
fore, that  Breuer's  explanation  of  the  apparent  motion 
of  optical  vertigo  is  correct,  and  also  that  this  move- 
ment cannot  be  made  to  disappear  by  the  voluntary 
fixation  of  the  eyes.  The  remaining  cases  of  optical 
vertigo  noticed  in  my  work  may  be  disposed  of  in  like 
manner.  1 

In  voluntary  forward  motion  or  rotation,  we  have 
not  only  a  sensation  of  every  single  successive  position 
of  the  parts  of  our  body,  but  also  the  much  more  sim- 
ple sensation  of  movement  forward  or  of  turning  round. 
As  a  fact,  we  do  not  form  the  notion  of  forward  move- 
ment from  the  percepts  of  the  various  individual  move- 
ments of  the  legs,  or  at  least  are  not  constrained  to  do 
so.  There  are  cases,  indeed,  in  which  the  sensation 
of  forward  movement  is  undoubtedly  present  while 
that  of  the  movements  of  the  legs  is  altogether  lack- 


1  Grundlinien  der  Lehre  von  den  Bewegungsempfindungen.  Leipsic,  Engel- 
mann,  1875.    P.  83. 


68  THE  ANALYSIS  OF  THE  SENSATIONS. 

ing.  This  is  true,  for  instance,  of  a  rail  way- journey, 
or  even  of  the  thought  of  such  a  journey,  and  may  oc- 
cur also  in  recalling  a  distant  place,  etc.  The  only 
possible  explanation  of  this  can  be  that  the  willio 
vaGve,  forward  or  to  turn  about,  which  furnishes  to  the 
extremities  their  motor  impulses, —  impulses  which 
may  be  further  modified  by  particular  innervations, — 
is  of  a  comparatively  simple  nature.  The  conditions 
existing  here  are  probably  similar  to,  although  more 
complicated  than,  those  connected  with  the  movements 
of  the  eyes,  which  Hering  has  so  felicitously  inter- 
preted, and  to  which  we  shall  presently  return. 

8. 

The  following  experiments  and  reflexions,  which 
form  a  sequel  to  an  earlier  publication  of  mine,  will 
perhaps  assist  us  in  obtaining  a  correct  view  of  these 
phenomena. 

If  we  take  our  stand  upon  a  bridge,  and  look  fix- 
edly at  the  water  flowing  beneath,  we  shall  generally 
have  the  sensation  of  being  ourselves  at  rest,  whilst 
the  water  will  seem  in  motion.  Prolonged  gazing, 
however,  almost  invariably  results  in  the  sensation 
that  suddenly  the  bridge,  with  the  observer  and  his 
whole  environment,  begins  to  move  in  the  direction 
opposite  to  that  of  the  water,  while  the  water  assumes 
the  appearance  of  being  at  rest.^     The  re/attve  motion 

lAs  we  all  know,  the  most  varied  forms  of  the  same  impression  are  ob- 
tained in  the  midst  of  a  nnmber  of  railway  trains  indiscriminately  in  motion 
and  at  rest.    A  short  time  ago,  while  making  a  steamboat  excursion  on  the 


SPACE-SENSATIONS  CONTINUED.  69 

of  the  objects  is  in  both  cases  the  same,  and  there 
must  therefore  be  some  adequate  physiological  reason 
why  at  one  time  one,  and  at  another,  another  part  of 
them  is  felt  to  move.  In  order  to  investigate  the  mat- 
ter at  my  leisure,  I  had  the  simple  apparatus  con- 
structed which  is  represented  in  Fig.  18.  An  oil-cloth 
of  simple  pattern  is  drawn  horizontally  over  two  rol- 
lers, two  metres  long  and  fixed  three  metres  apart  in 
bearings,  and  is  kept  in  uniform  motion  by  means  of  a 
crank.  Across  the  oil-cloth 
and  about  thirty  centime- 
tres above  it,  is  stretched 
a  string  ff,  with  a  knot  K, 
which  serves  as  a  fixation- 
point  for  the  eye  of  the 
observer  stationed  at  A. 
Now,  if  the  oil-cloth  be  set 
in  motion  in  the  direction  of  the  arrow,  and  the  ob- 
server follow  the  pattern  with  his  eyes,  he  will  see  it  in 
motion,  himself  and  his  surroundings  at  rest.  On  the 
other  hand,  if  he  gazes  at  the  knot,  he  and  the  whole 
room  will  presently  appear  in  motion  in  the  contrary 
direction  to  the  arrow,  while  the  oil-cloth  will  stand 
still.  This  change  in  the  aspect  of  the  motion  takes 
more  or  less  time  according  to  the  mental  condition 
of  the  observer,  but  usually  requires  only  a  few  sec- 
onds.    If  we  once  get  the  knack  of  it,  the  two  impres- 

Elbe,  I  was  astonished  at  discovering,  just  before  landing,  that  the  ship  was 
standing  still  and  that  the  whole  landscape  was  moving  towards  it — an  expe- 
rience that  will  be  readily  understood  from  what  follows. 


70  THE  ANALYSIS  OF  THE  SENSATIONS. 

sions  may  be  made  to  alternate  with  some  rapidity 
and  at  will.  Every  following  of  the  oil-cloth  brings 
the  observer  to  rest,  every  fixation  of  Ky  or  non-atten- 
tion to  the  oil-cloth,  by  which  its  pattern  becomes 
blurred,  sets  the  observer  in  motion.  This  phenom- 
enon, of  course,  must  not  be  confounded  with  the  fa- 
miliar Plateau-Oppel  phenomenon,  which  is  a  local  x^- 
tinal  effect.  In  the  preceding  experiment,  the  entire 
environment,  so  far  as  it  is  distinctly  visible,  is  in  mo- 
tion, whilst  in  the  latter  a  moving  veil  is  drawn  along 
in  front  of  the  object,  which  is  at  rest.  The  attendant 
stereoscopic  phenomena, — for  example,  the  appear- 
ance of  the  thread  and  knot  underneath  the  transparent 
oil-cloth, — are  quite  immaterial  in  this  connexion. ^ 

Before  we  proceed  to  the  explanation  of  the  expe- 
riment, it  will  be  well  to  introduce  a  few  variations. 
An  observer  stationed  at  B  seems,  under  the  same 
conditions,  to  be  speeding,  with  all  his  surroundings, 
towards  the  left.  We  now  place  above  the  oil-cloth 
TTy  Fig.  19,  a  mirror  SS,  inclined  at  an  angle  of  45° 
to  the  horizon.  We  observe  the  reflexion  TT  in  SS, 
after  having  placed  on  our  nose  a  shade  nn,  which  in- 

1  In  my  book  on  Bewegungsempfindungen  (p.  63)  I  stated  that  the  Plateau- 
Oppel  phenomenon  was  the  result  of  a  peculiar  process,  which  was  not  con- 
cerned in  the  other  sensations. of  movement.    I  wrote  there  as  follows  : 

"We  must  therefore  suppose  that,  during  the  movement  of  an  image  on 
the  retina,  z.  peculiar  process  is  excited  which  is  absent  during  rest,  and  that 
in  the  case  of  movements  in  opposite  directions,  very  similar  processes  are  ex- 
cited in  similar  organs,  processes  which  are,  however,  mutually  exclusive,  so 
that  with  the  commencement  of  the  one,  the  other  must  cease,  and  with  the 
exhaustion  of  the  one,  the  other  begins." 

This  statement  of  mine  seems  to  have  been  overlooked  by  S.  Exner  and 
Vierordti  who  subsequently  expressed  similar  views  on  the  same  subject, 


>^K 


SPACE-SENSATIONS  CONTINUED.  71 

tercepts  the  direct  view  of  TT  from  the  eye,  O.  If 
TT  moves  in  the  direction  of  the  arrow,  while  we  are 
looking  at  K',  the  reflexion  of  K,  we  shall  presently 
fancy  ourselves  sinking  downward  with  the  whole 
room,  whereas  if  the  motion  be 
reversed  we  shall  seem  to  ascend         i   y^Rf  yyn^ 

as  if  in  a  balloon.^  Finally,  the 
experiments  with  the  paper  drum, 
which  I  have  elsewhere  described, 
and    to  which   the   following  ex-        ^  ^ 

planation  also  applies,  should  be 

cited  here.  None  of  these  phenomena  are  purely  op- 
tical^ but  all  are  accompanied  by  unmistakable  motor 
sensations  of  the  whole  body. 

9- 

What  form,  now,  must  our  thoughts  take  on,  in  or- 
der to  acquire  the  simplest  explanatory  setting  for  the 
preceding  phenomena?  Objects  in  motion  exert,  as  is 
well  known,  a  peculiar  motor  stimulus  upon  the  eye, 
and  draw  our  attention  and  look  after  them.  If  the  eye 
really  follows  them,  we  must  assume,  from  what  has 
gone  before,  that  the  objects  move.  But  if  the  eye  is 
kept  at  rest,  and  is  forcibly  restrained  from  following 
the  moving  objects,  the  constant  stimulus  to  motion 
proceeding  from  the  latter  must  be  counterbalanced 

1  Such  phenomena  often  make  their  appearance  quite  unsought.  As  my 
little  daughter  was  once  standing  near  a  window,  on  a  calm  winter's  day, 
during  a  heavy  snow-fall,  she  suddenly  cried  out  that  she  was  rising  upward 
with  the  whole  house. 


72  THE  ANALYSIS  OF  THE  SENSATIONS. 

by  an  equally  constant  stream  of  innervation  flowing 
to  the  motor  apparatus  of  the  eye,  exactly  as  if  the 
motionless  point  on  which  the  eyes  rest  were  moving 
uniformly  in  the  opposite  direction,  and  we  were  fol- 
lowing that  with  our  eyes.  But  when  this  process  be- 
gins, all  motionless  objects  on  which  the  eyes  are  fast- 
ened must  appear  in  motion.  It  is  obviously  unneces- 
sary that  this  stream  of  innervation  should  always  be 
consciously  and  deliberately  called  into  action.  All 
that  is  requisite  is  that  it  should  proceed  from  the 
same  centre  and  by  the  same  paths  as  intentional  fixa- 
tion. 

No  special  apparatus  is  necessary  for  observing 
the  foregoing  phenomena.  They  are  to  be  met  with 
on  all  hands.  I  walk  forward  by  a  simple  act  of  the 
will.  My  legs  perform  their  functions  without  special 
intervention  on  my  part.  My  eyes  are  fixed  stead- 
fastly upon  their  goal  without  suffering  themselves  to 
be  drawn  aside  by  the  motion  of  the  retinal  images 
consequent  upon  progression.  All  this  is  brought 
about  by  a  single  act  of  the  will,  and  this  act  of  the 
will  itself  is  the  sensation  of  forward  movement.  The 
same  process,  or  at  least  a  part  of  it,  must  also  be  set 
up,  if  the  eyes  are  made  to  resist  permanently  the  ex- 
citation of  a  mass  of  moving  objects.  Hence  the  motor 
sensations  experienced  in  the  foregoing  experiments. 

The  eyes  of  a  child  on  a  railway-train  will  be  ob- 
served to  follow  almost  uninterruptedly  and  with  a 
jerking  motion  the  objects  outside,  which  appear  to  it 


SPACE-SENSATIONS  CONTINUED.  73 

to  be  running.  The  adult  has  the  same  sensation  if 
he  will  passively  yield  himself  to  the  natural  impres- 
sions. If  I  am  riding  forwards,  the  whole  space  to  my 
left,  for  obvious  reasons,  rotates,  in  the  direction  of  the 
hands  of  a  watch,  about  a  very  distant  vertical  axis, 
and  the  space  to  my  right  does  the  same,  but  in  the 
opposite  direction.  Only  when  I  resist  following  the 
objects  with  my  eyes,  does  the  sensation  of  forward 
motion  arise. 

10. 

Without  doing  violence  to  the  facts  described  in 
my  book  on  The  Sensations  of  Movement^  the  preceding 
observations  suggest  the  possibility  of  modifying  the 
theoretical  view  there  taken  of  the  facts,  as  we  shall 
point  out  in  the  following.^     It  is  extremely  probable 

IMy  views  regarding  the  sensations  of  movement  have  been  repeatedly 
attacked,  as  is  well  known,  but  invariably  the  adverse  arguments  have  been 
aimed  solely  at  the  hypothesis,  to  which  I  attached  comparatively  little  im- 
portance. That  I  am  ready  and  willing  to  modify  my  views  in  accordance 
with  newly  discovered  facts,  the  present  work  will  testify.  The  decision  as 
to  how  far  I  am  in  the  right  I  will  cheerfully  leave  to  the  future.  On  the  other 
hand,  observations  have  been  made  that  strongly  favor  the  theory  propounded 
by  myself,  Breuer,  and  Brown.  To  these  belong,  first,  the  facts  collected  by 
Dr.  Guye  of  Amsterdam  [Du  Vertige  de  Meniere:  Rapport  lu  dans  la  section 
d  "otologie  du  congres  piriodique  international  de  sciences  tnidicales  h  Amster- 
dam, 1879).  Guye  observed,  in  diseases  of  the  middle  ear,  that  reflex  turnings 
of  the  head  were  induced  when  air  was  blown  into  the  cavity  of  the  tympa- 
num, and  found  a  patient  who  was  able  to  state  exactly  the  direction  and 
number  of  the  turnings  v/hich  he  had  felt  during  the  injection  of  liquids, 
—Prof.  Crum  Brown  ("On  a  Case  of  Dyspeptic  Vertigo,"  Proceedings  of  the 
Royal  Society  of  Edinburgh,  1881-1882),  has  described  an  interesting  case  of 
pathological  vertigo  observed  in  himself,  which  admitted  of  explanation,  as 
a  whole,  by  the  increased  intensity  and  lengthened  duration  of  the  sensation 
incident  upon  every  turning  of  the  body.— But  most  remarkable  of  all  are  the 
observations  of  William  James  ("The  Sense  of  Dizziness  in  Deaf-Mutes,' 
American  Journal  of  Otology,  Vol.  IV.,  1882).  James  discovered  in  deaf-mutes 
a  striking  and  relatively  general  insensibility  to  the  dizziness  of  whirling, 


74  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

that  an  organ  exists  in  the  head — it  may  be  called  the 
terminal  organ  {TO) — which  reacts  upon  accelerations ^ 

often  great  uncertainty  in  their  walk  when  their  eyes  were  closed,  and  in 
many  cases  an  astonishing  loss  of  the  sense  of  direction  on  being  plunged  un- 
der water,  in  which  case  there  always  resulted  alarm  and  complete  uncertainty 
as  to  up  and  down.  These  facts  speak  very  strongly  in  favor  of  the  view,  which 
naturally  follows  from  my  conception,  that  in  deaf-mutes  the  sense  of  equi- 
librium proper  is  considerably  degenerated,  and  that  the  two  other  localising 
senses,  the  sense  of  sight  and  the  muscular  sense,  (the  latter  of  which  loses 
all  its  points  of  reference  when  the  weight  of  the  body  is  neutralised  by  im- 
mersion in  water,)  are  rendered  proportionately  more  necessary. 

The  view  is  untenable  that  we  arrive  at  knowledge  of  equilibrium  and  of 
movement  solely  by  means  of  the  semi-circular  canals.  On  the  contrary,  it  is 
extremely  probable  that  lower  animals,  in  whom  this  organ  is  entirely  want- 
ing, also  have  sensations  of  movement.  I  have  not  yet  been  able  to  under- 
take experiments  in  this  direction.  But  the  experiments  which  Lubbock  has 
described  in  his  work,  Ants,  Bees,  and  Wasps,  become  much  more  compre- 
hensible to  me  on  the  assumption  of  sensations  of  movement.  As  experi- 
ments of  this  sort  may  be  interesting  to  others,  it  will  not  be  amiss  perhaps  to 
consider  an  apparatus  which  I  have  briefly  described  before  {Anzeiger  der 
Wiener  Akademie,  December  30,  1875). 

The  apparatus  serves  for  the  observation  of  the  conduct  of  animals  while 
in  rapid  rotation.  Since,  however,  the  view  of  the  animal  will  necessarily  be 
eflfaced  by  the  rotary  motion,  the  passive  rotation  must  be  optically  nullified 
and  eliminated,  so  that  the  active  movements  of  the  animal  alone  shall  be 
left  and  rendered  observable.  The  optical  neutralisation  of  the  rotary  mo- 
tion is  attained  simply  by  causing  a  totally  reflecting  prism  to  revolve,  with 
the  aid  of  gearing,  above  the  disk  of  the  whirling  machine,  about  exactly 
the  same  axis,  in  the  same  direction,  and  with  half  the  angular  velocity  of  the 
disk. 

Fig.  20  gives  a  view  of  the  apparatus.  On  the  disk  of  the  whirling  ma- 
chine is  a  glass  receiver,  g,  in  which  the  animals  to  be  observed  are  enclosed. 
By  means  of  gearing  the  eye-piece  o  is  made  to  revolve  with  half  the  angular 
velocity  and  in  the  same  direction  as^.  The  following  figure  gives  the  gear- 
ing in  a  separate  diagram.  The  eye-piece  00,  and  the  receiver  gg,  revolve 
about  the  axis  AA,  while  a  pair  of  cog-wheels,  rigidly  connected  together,  re- 
volve  about  BB.  Let  the  radius  of  the  cog-wheel  aah&r;  that  of  bb  also  r, 
that  of  cc  2^/3,  and  that  of  dd  4^/3,  wherewith  the  desired  relation  of  velo- 
city between  00  and  gg  is  obtained. 

In  order  to  centre  the  apparatus,  a  mirror  S,  provided  with  levelling- 
screws,  is  laid  upon  the  bottom  of  the  receiver  and  so  adjusted  that,  on  rota- 
tion, the  reflexions  in  it  remain  at  rest.  It  is  then  perpendicular  to  the  axis 
of  rotation.  A  second  small  mirror,  S',  in  the  silvering  of  which  is  a  small 
hole  L,  is  so  adjusted  to  the  open  tube  of  the  eye-piece,  with  its  reflecting  sur- 
face downward,  that,  on  rotation,  the  images  seen  through  the  hole,  in  the 
mirrored  reflexion  of  S'  in  S,  remain  motionless.  Then  S'  stands  perpendicu- 
lar to  the  axis  of  the  eye-piece.  With  the  aid  of  a  brush  we  may  now  mark 
upon  the  mirror  S  a  point  P,  whose  position  is  not  altered  on  rotation  (a  re- 


SPACE-SENSATIONS  CONTINUED. 


75 


and  by  means  of  which  we  are  made  aware  of  move- 
ments.    But  instead  of  imagining  that  special  motor 

suit  which  is  easily  accomplished  after  a  few  trials),  and  so  place  the  hole  in 
the  mirror  S'  that  it  also  remains  stationary  on  rotation.    In  this  way  points 


111  1 1 1 1 1 1 


n 


Fig.  21. 


Fig.  20. 

on  both  axes  of  rotation   are   found.     If  now— by  means  of  screws— we  so 

adjust  the  eye-piece,  that,  on  looking  through  the  hole  in  5',  the  point  PonS 

and  the  reflexion  ofZ,  in  \ 

S'  (or  really  the  many  ;-4  ] 

reflexions  of  P  and  L)  n  \  n  k^ 

fall  on  the  same  spot, 

then  the  two  axes  are 

not  only   parallel    but 

coincident. 

The  simplest  eye- 
piece that  can  be  em- 
ployed, is  a  mirror 
whose  plane  coincides 
with  the  axis,  and  I 
adopted  this  device  in 
the  initial  form  of  my 
apparatus.  But  one-half 
of  the  field  of  vision  is 
lost  by  this  method.  A  prism  of  total  reflexion,  therefore,  is  much  more  ad- 
vantageous.   Let  ABC  {Fig.  22)  represent  a  plane  section  of  such  a  prismatic 


76  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

sensations  exist,  which  proceed  from  this  apparatus  as 
from  a  sense-organ,  we  may  assume  that  this  organ 
simply  disengages  innervations  after  the  manner  of  re- 
flexes. Innervation  may  be  voluntary  and  conscious 
or  involuntary  and  unconscious.  The  two  different 
organs  from  which  these  proceed  may  be  designated 
by  the  letters  WI  and  UI.     Both  sorts  of  innervation 


eye-piece  cut  perpendicularly  to  the  planes  of  the  hypothenuse  and  the  two 
sides.  Let  this  section  include,  also,  the  axis  of  rotation  ONPQ,  which  is 
parallel  to  AB.  The  ray  which  passes  along  the  axis  QP  must,  after  refrac- 
tion and  reflexion  in  the  prism,  proceed 
again  along  the  axis  NO  and  will  meet 
the  eye  O  in  the  prolongation  of  the  axis. 
This  done,  the  points  of  the  axis  can  suf- 
fer no  displacement  from  rotation,  and 
the  apparatus  is  centred.  The  ray  in 
question  must  accordingly  fall  at  M,  the 
middle  point  of  AB,  and,  hence,  since  it 
falls  on  crown  glass  at  an  angle  of  inci- 
dence of  45°,  will  meet  .^5  at  about  i6° 
40'.  Therefore,  OP  must  be  distant  about 
0-115  AB  from  the  axis,— a  relation  which 
can  best  be  obtained  by  trial,  by  so  mov- 
ing the  prism  in  the  eye-piece  that  os- 
cillations of  the  objects  in^^  during  ro- 
tation are  eliminated. 

Fig.  22  also  shows  the  field  of  vision 
for  the  eye  at  O.  The  ray  OA,  which 
falls  vertically  upon  AC,  is  reflected  at 
AB  in  the  direction  AC  and  passes  out 
towards  S.  The  ray  OR,  on  the  other 
hand,  is  reflected  at  B  and  emerges,  after 
refraction,  in  the  direction  of  T. 
The  apparatus  has  hitherto  proved  quite  suflicient  for  my  experiments.  If 
a  printed  page  is  placed  in^^,  and  the  apparatus  turned  so  rapidly  that  the 
image  on  the  retina  is  entirely  obliterated,  one  can  easily  read  the  print 
through  the  eye-piece.  The  inversion  of  the  image  by  reflexion  could  be  re- 
moved by  placing  a  second,  stationary  reflecting  prism  above  the  revolving 
prism  of  the  eye-piece.  But  this  complication  appeared  to  me  unnecessary. 
With  the  exception  of  a  few  physical  experiments,  I  have  hitherto  under- 
taken rotation-experiments  only  with  various  small  vertebrates  (birds,  fishes), 
and  have  found  the  data  given  in  my  work  on  Motor  Sensations  fully  con- 
firmed. However,  it  would  probably  be  of  advantage  to  make  similar  experi- 
ments with  insects  and  other  lower  animals,  especially  with  marine  animals. 


Fig.  22. 


SPACE-SENSATIONS  CONTINUED.  'j'j 

may  pass  to  the  oculo-motor  apparatus  {^OM')  and  to 
the  locomotor  apparatus  {LM^. 

Let  us  now  consider  the  accompanying  diagram. 
We  induce  by  the  will,  that  is  by  a  stimulus  from  WI, 
an  active  movement,  which  passes  in  the  direction  of 
the  unfeathered  arrows,  to  OM  and  LM.  The  appur- 
tenant innervation  is  directly  felt.  In  this  case,  there- 
fore, a  special  sensation  of  movement,  differing  from 
the  innervation,  is  unnecessary.  If  the  motion  in  the 
direction  of  the  unfeathered  arrows  is  a  passive  one 

(taking    us     by    sur-  ^  ^ 

prise),  then,  as  ex- 
perience shows,  re- 
flexes proceed  from 
TO  over  UI,  which 
produce  compensa- 
tory movements,  indi- 
cated by  the  feathered  ^^^'  ^^' 
arrows.  If  WI  takes  no  part  in  the  process,  and  the 
compensation  is  effected,  both  the  motion  and  the  ne- 
cessity for  motor  sensation  cease.  But  if  the  compen- 
satory movement  is  intentionally  suppressed,  that  is, 
by  intervention  from  Wly  then  the  same  innervation  is 
necessary  for  achieving  this  result  as  for  active  move- 
ment, and  it  consequently  produces  the  same  motor 
sensation. 

The  terminal  organ  TO  is  accordingly  so  adjusted 
to  WI  and  UI  that  upon  a  given  motor  stimulus  in 
the  first,  contrary  innervations  are  set  up  in  the  last 


78  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

two.  But  further,  we  have  to  notice  the  following  dif- 
ference in  the  relation  of  TO  to  WI  and  UI.  For 
TOi  the  motor  excitation  is  naturally  the  same  whether 
the  movement  induced  is  passive  or  active.  In  active 
movements,  too,  the  innervations  proceeding  from  WI 
would  eventually  be  neutralised  by  TO  and  UI,  did  not 
inhibitory  innervations  proceed  simultaneously  with 
the  willed  innervations  from  WIX.0  TO  and  UL  The 
influence  of  TO  upon  WI  must  be  conceived  as  much 
weaker  than  that  of  TO  upon  UI.  If  we  should  picture 
to  ourselves  three  animals,  WI,  UI,  and  TO,  between 
whom  there  was  a  division  of  labor,  such  that  the  first 
executed  only  movements  of  attack,  the  second  only 
those  of  defence  or  flight,  while  the  third  filled  the 
post  of  sentinel,  all  of  whom  were  united  into  a  single 
new  organism  in  which  ^/held  the  dominant  position, 
we  should  have  a  conception  approximately  corre- 
sponding to  the  relation  represented.  There  is  much 
in  favor  of  such  a  conception  of  the  higher  animals.^ 
I  do  not  offer  the  preceding  view  as  a  complete  and 
perfectly  apposite  picture  of  the  facts.  On  the  con- 
trary, I  am  fully  aware  of  the  defects  in  my  treatment. 

llf  I  grasp  a  little  bird  in  my  hand,  the  bird  will  behave  towards  my  hand 
exactly  as  a  human  being  would  towards  a  giant  cuttle-fish. — In  watching  a 
company  of  little  children  whose  movements  are  largely  unreflecting  and  un- 
practised, the  hands  and  eyes  remind  one  very  strongly  of  polyphoid  crea- 
tures. Of  course,  such  impressions  do  not  afford  solutions  of  scientific  ques- 
tions, but  it  is  often  very  suggestive  to  abandon  oneself  to  their  influence. 

(A  welcome  confirmation  of  my  conjecture  of  1875  regarding  the  macula 
acustica  has  been  furnished  by  the  subsequent  works  of  Breuer  and  Kreidl. 
The  latter  has  succeeded  in  causing  certain  specimens  of  the  Crustacea  to 
substitute  ferrum  limatum  for  their  natural  otoliths,  and  they  have  then  re- 
acted on  magnets  by  changes  of  position. — Mach,  1896.] 


SPACE-SENSATIONS  CONTINUED.  79 

But  the  attempt  to  reduce  to  a  quality  of  sensation,  in 
accordance  with  the  cardinal  principle  evolved  in  our 
investigation  (p.  28),  all  sensations  of  space  and  move- 
ment arising  in  the  province  of  sight  and  touch  during 
change  of  place,  or  even  as  a  shadow  in  remembrance 
of  locomotion,  or  at  the  thought  of  a  distant  spot,  etc., 
will  be  found  justifiable.  The  assumption  that  this 
quality  of  sensation  is  the  will,  so  far  as  the  latter  is 
occupied  with  position  in  space  and  spatial  relation, 
or  the  sensation  of  innervation,  does  not  forestall  fu- 
ture investigation  and  only  represents  the  facts  as  they 
are  known  at  the  present  time.^ 

II. 
From  the  discussions  of  the  previous  chapter  rela- 
tive to  symmetry  and  similarity,  we  may  immediately 
draw  the  conclusion  that  to  like  directions  of  lines 
which  are  seen,  the  same  kind  of  innervation-sensa- 
tions,  and  to  lines  symmetrical  with  respect  to  the 
median  plane  very  similar  sensations  of  innervation 
correspond,  but  that  with  looking  upwards  and  look- 
ing downwards,  or  with  looking  at  objects  afar  off  and 
at  the  objects  near  at  hand,  very  different  sensations 
of  innervation  are  associated, — as  we  should  naturally 
be  led  to  expect  from  the  symmetrical  arrangement  of 
the  motor  apparatus  of  the  eye.  With  this  single  per- 
ception we  dispose  of  a  long  chain  of  peculiar  physi- 
ologico-optical  phenomena,  which  have  as  yet  received 

1  Compare  Hering's  opinion  given  in  Hermann's  Handbuch  der  Physiologu, 
Vol.  III.,  Part  I.,  p.  547. 


8o  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

scarcely  any  attention.   I  now  come  to  the  point  which, 
physically  regarded  at  least,  is  the  most  important. 

The  space  of  the  geometrician  is  a  mental  construct 
of  threefold  manifoldness,  that  has  grown  up  on  the 
basis  of  manual  and  intellectual  operations.  Optical 
space  (Hering's  "  sight -space ")  bears  a  somewhat 
complicated  geometrical  relationship  to  the  former. 
The  matter  may  be  best  expressed  in  familiar  terms  by 
saying  that  optical  space  represents  geometrical  space 
(Euclid's  space)  in  a  sort  of  relievo-perspective — a  rela- 
tion of  things  which  may  be  teleologically  explained. 
In  any  event,  optical  space  also  is  a  threefold  mani- 
foldness. The  space  of  the  geometrician  exhibits  at 
every  point  and  in  all  directions  the  same  properties — 
a  quality  which  is  by  no  means  characteristic  of  phys- 
iological space.  But  the  influence  of  physiological 
space  may  nevertheless  be  abundantly  observed  in  ge- 
ometry. Such  is  the  case,  for  example,  when  we  dis- 
tinguish between  convex  and  concave  curvatures.  The 
geometrician  should  really  know  only  the  amount  of 
deviation  from  the  mean  of  the  ordinates. 

12. 

As  long  as  we  conceive  the  (12)  muscles  of  the  eye 
to  be  separately  innervated,  we  are  not  in  a  position 
to  explain  this  fundamental  fact.  I  felt  this  difficulty 
for  years,  and  also  recognised  the  direction  in  which, 
on  the  principle  of  the  parallelism  of  the  physical  and 
the  psychical,  the  explanation  was  to  be  sought ;  but 


SPACE-SENSATIONS  CONTINUED.  8i 

owing  to  my  defective  experience  in  this  province,  the 
solution  itself  remained  hidden  from  me.  All  the  bet- 
ter, therefore,  am  I  able  to  appreciate  the  service  ren- 
dered by  Hering,  who  discovered  it.  To  the  three 
optical  space  co-ordinates,  viz.,  to  the  sensations  of 
height,  breadth,  and  depth,  corresponds  according  to 
the  showing  of  this  investigator  (Hering,  Beitrdge  ziir 
Fhysiologie,  Leipsic,  Engelmann,  1861-1865)  simply  a 
threefold  innervation,  which  turns  the  eyes  to  the  right 
or  to  the  left,  raises  or  lowers  them,  and  causes  them 
to  converge,  according  to  the  respective  needs  of  the 
case.  This  is  the  point  which  I  regard  as  the  most 
important  and  essential.  ^  Whether  we  regard  the  in- 
nervation itself  as  the  space-sensation,  or  whether  we 
conceive  the  space-sensation  as  ulterior  to  the  inner- 
vation,— a  question  neither  easy  nor  necessary  to  de- 
cide,— nevertheless  Hering's  statement  throws  a  flood 
of  light  on  the  psychical  obscurity  of  the  visual  pro- 
cess. The  phenomena  cited  by  myself  with  regard  to 
symmetry  and  similarity,  moreover,  accord  excellently 
with  this  conception.  But  it  is  unnecessary,  I  think, 
to  substantiate  further  their  agreement.  ^ 

IThis  is  the  point  to  which  reference  was  made  above  (p.  57  and  page  68). 

2  This  conception  also  removes  a  difficulty  which  I  still  felt  in  1871,  and 
to  which  I  gave  utterance  in  my  lecture  on  "  Symmetry  "  (Prague :  Calve 
1872), — now  translated  into  English  in  my  Popular  Scientific  Lectures,  Chicago, 
1894,— in  the  following  words :  "The  possession  of  a  sense  for  symmetry  by 
persons  who  are  one-eyed  from  birth  is  certainly  an  enigma.  Yet  the  sense 
for  symmetry,  although  originally  acquired  by  the  eyes,  could  not  have  been 
confined  exclusively  to  the  visual  organs.  By  thousands  of  years  of  practice 
it  must  also  have  been  implanted  in  other  parts  of  the  human  organism,  and 
cannot,  therefore,  be  immediately  eliminated  on  the  loss  of  an  eye."  As  a  fact, 
the  symmetrical  apparatus  of  innervation  remains,  even  when  one  eye  is  lost. 


THE  SIGHT-SENSATIONS. 


THEIR    RELATIONS    TO   ONE   ANOTHER   AND   TO 
OTHER  PSYCHICAL  ELEMENTS. 

I. 

TN  normal  psychical  life,  sight -sensations  do  not 
-^  make  their  appearance  alone,  but  are  accompa- 
nied by  other  sensations.  We  do  not  see  optical  im- 
ages in  an  optical  space,  but  we  perceive  the  bodies 
round  about  us  in  their  many  and  varied  sensuous 
qualities.  Deliberate  analysis  is  needed  to  single  out 
the  sight-sensations  from  these  complexes.  Even  the 
total  perceptions  themselves  are  almost  invariably  ac- 
companied by  thoughts,  wishes,  and  impulses.  By 
sensations  are  excited,  in  animals,  the  movements  of 
adaptation  demanded  by  their  conditions  of  life.  If 
these  conditions  are  simple,  altering  but  little  and 
slowly,   immediate    sensory    excitation   is    sufficient.^ 


IBearing  this  circumstance  in  mind,  will  prevent  onr  overestimating  the 
intelligence  of  lower  species. 

[When  the  above  lines  were  written,  over  ten  years  ago,  I  had  only  a  few 
experiences  of  my  own  at  command.  I  knew  that  certain  beetles  crept  only 
upwards  on  stalks,  no  matter  how  often  they  were  turned  round,  that  when 
they  arrived  at  tke  top  they  again  invariably  flew  upwards;  that  moths  always 


RELATIONS  OF  THE  SIGHT-SENSATIONS.         83 

Higher  intellectual  development  is  unnecessary.  But 
the  case  is  different  where  the  conditions  of  life  are 
intricate  and  variable.  Here  so  simple  a  mechanism 
of  adaptation  can  neither  develop,  nor  would  it  lead 
to  the  accomplishment  of  the  required  ends. 

Lower  species  devour  everything  that  comes  in 
their  way  and  that  excites  the  proper  stimulus.  A 
more  highly  developed  animal  must  seek  its  food  at 
risks  to  itself ;  when  found,  must  seize  it  at  the  right 
spot,  or  capture  it  by  cunning,  and  cautiously  test  its 
character.  Long  trains  of  varied  memories  must  pass 
before  its  mind  before  one  is  sufficiently  strong  to  out- 
weigh the  antagonistic  considerations  and  to  excite  the 
appropriate  movement.  Here,  therefore,  a  sum  of 
associated  remembrances  (or  experiences)  coincidently 
determining  the  adaptive  movements,  accompany  and 
confront  the  sensations.    In  this  consists  the  intellect. 

In  the  young  of  higher  animals,  presenting  com- 
plex conditions  of  life,  the  complexes  of  sensations  nec- 
essary to  excite  adaptive  movements  are  frequently 
of  a  very  complicated  nature.^  With  the  development 
of  intelligence,  the  parts  of  these  complexes  necessary 

flew  towards  the  light ;  in  short,  that  certain  animals  often  acted  under  certain 
circumstances  like  automata.  Since  then  much  light  has  been  thrown  en  this 
subject,  and  by  none  more  than  by  the  beautiful  researches  of  J.  Loeb  on 
Geotropismus  and  Heliotropismus.  Arrogant  underestimation  of  the  intelli- 
gence of  animals  has  frequently  alternated  with  irrational  overestimation  of 
their  powers.  I  regard  it  as  a  great  service  on  Sir  John  Lubbock's  part  to 
have  paved  the  way,  by  his  experiments  on  bees  and  ants,  for  more  correct 
ideas  on  this  subject.  I  also  accept  here  in  all  essential  points  the  views  of 
C.  Lloyd  Morgan. — Mach,  1895. 1 

IThe  sucking  of  young  mammals,  and  the  conduct  of  the  young  sparrow 
described  in  the  note  on  page  37  are  good  examples  of  this. 


84  THE  ANALYSIS  OF  THE  SENSATIONS. 

to  produce  the  excitation  constantly  diminish,  and  the 
sensations  are  more  and  more  supplemented  and  re- 
placed by  the  intellect,  as  may  be  daily  observed  in 
children  and  adolescent  animals. 

2. 

Representation  by  images  and  ideas,  therefore,  has 
to  supply  the  place  of  sensations,  where  the  latter  are 
imperfect,  and  to  carry  to  their  issue  processes  ini- 
tially determined  by  sensations  alone.  But  in  normal 
life,  representation  cannot  supplant  sensation,  where 
this  is  at  all  present,  except  with  the  greatest  danger 
to  the  organism.  As  a  fact,  there  is,  in  normal  psy- 
chical life,  a  marked  difference  between  the  two  spe- 
cies of  psychical  factors.  I  see  a  blackboard  before 
me.  I  can,  with  the  greatest  vividness,  represent  to 
myself  on  this  blackboard,  either  a  hexagon  drawn  in 
clear,  white  lines,  or  a  colored  figure.  But,  pathologi- 
cal cases  apart,  I  always  distinguish  what  I  see  and 
what  I  represent  to  myself.  In  the  transition  to  repre- 
sentation, I  am  aware  that  my  attention  is  turned  from 
my  eyes,  and  directed  elsewhere.  In  consequence  of 
this  attention,  the  spot  seen  upon  the  blackboard  and 
the  one  represented  to  myself  as  situated  in  the  same 
place  differ  as  by  a  fourth  co-ordinate.  It  would  not 
be  a  complete  description  of  the  facts  to  say  that  the 
representation  overlays  the  object  as  the  images  re- 
flected in  a  transparent  plate  of  glass  overlay  the  bod- 
ies seen  through  it.     We  are  confronted  here,  for  the 


RELATIONS  OF  THE  SIGHT-SENSATIONS,         85 

time  being,  with  a  fundamental  psychological  fact, 
the  physiological  explanation  of  which  will  sometime 
undoubtedly  be  discovered. 

Where  the  development  of  intelligence  has  reached 
a  high  point,  such  as  is  presented  now  in  the  com- 
plex conditions  of  human  life,  representation  may  fre- 
quently absorb  the  whole  of  attention,  so  that  events 
in  the  neighborhood  of  the  reflecting  person  are  not 
noticed,  and  questions  addressed  to  him  are  not  heard  ; 
— a  state  which  persons  unused  to  it  are  wont  to  call 
absent-mindedness,  although  it  might  with  more  ap- 
propriateness be  called  present-mindedness.  If  the 
person  in  question  is  disturbed  in  such  a  state,  he  has 
a  very  distinct  sensation  of  the  labor  involved  in  the 
transference  of  his  attention. 

3. 

It  is  well  to  note  this  sharp  division  between  rep- 
resentations and  sensations,  as  it  is  an  excellent  safe- 
guard against  carelessness  in  psychological  explana- 
tions of  sense-phenomena.  The  well-known  theory 
of  "  unconscious  reasoning"  would  never  have  reached 
its  present  extended  development  if  more  heed  had 
been  paid  to  this  circumstance. 

The  organ  of  representation  can  for  the  nonce  be 
conceived  as  one  which,  in  a  diminished  degree,  is 
susceptible  of  all  the  specific  energies  of  the  sense 
and  motor  organs,  so  that,  according  to  the  special 
attention  evoked,  now  this,  now  that  specific  energy 


86  THE  ANALYSIS  OF  THE  SENSATION.%, 

is  excited  in  it.  Such  an  organ  is  eminently  qualified 
for  physiological  mediation  between  the  different  en- 
ergies. As  is  shown  by  experiments  with  animals 
whose  cerebrum  has  been  removed,  there  are  prob- 
ably, in  addition  to  the  organ  of  representation,  a 
number  of  other,  analogous  organs  of  mediation,  whose 
processes  are  unconscious. 

That  wealth  of  representative  life  with  which  we  are 
personally  acquainted  from  self-observation,  doubtless 
made  its  first  appearance  with  man.  But  the  begin- 
nings of  this  expression  of  life,  in  which  nothing  but 
the  relations  of  the  various  parts  of  the  organism  to 
one  another  is  manifested,  go  back  with  no  less  cer- 
tainty to  quite  primitive  stages  in  the  animal  scale. 
On  the  other  hand,  the  parts  of  single  organs  must  also, 
by  mutual  adaptation,  sustain  a  reciprocal  relation  to 
one  another  analogous  to  that  of  the  parts  of  the  or- 
ganism as  a  whole.  The  two  retinas,  with  their  motor 
mechanism  of  accommodation  and  of  luminous  adjust- 
ment, controlled  by  light  sensations,  afford  a  very 
clear  and  familiar  example  of  such  a  relation.  Physio- 
logical experiment  and  simple  self-observation  teach 
us  that  such  an  organ  has  its  own  adaptive  habits,  its 
own  peculiar  memory,  one  might  almost  say  its  own 
intelligence. 

The  most  instructive  observations  in  this  connex- 
ion are  probably  those  of  Johannes  MuUer,  collected 
in  his  excellent  work  on  '*The  Phantasms  of  Sight*' 
(JJeber  die  phantasiischen  Gesichtserscheinungen.     Cob* 


RELATIONS  OF  THE  SIGHT-SENSATIONS.         87 

lenz,  1826).  The  sight-phantasms  observed  by  Miiller 
and  others  in  the  waking  state  are  entirely  without  the 
control  of  either  the  will  or  the  reason.  They  are  in- 
dependent phenomena,  connected  not  with  the  organ 
of  representation,  but  with  the  sense-organs,  and  have 
thoroughly  the  character  of  processes  objectively  seen. 
They  are  veritable  imagination  and  memory  phenom- 
ena of  sense. 

Those  processes  which  (according  to  MuUer)  are 
normally  induced  in  the  visual  substance  by  excita- 
tions of  the  retina,  and  which  condition  the  act  of 
seeing,  may  also,  under  certain  conditions,  be  spon- 
taneously produced  in  the  visual  substance  without 
excitation  of  the  retina,  becoming  there  the  source 
of  phantasms  or  hallucinations.  We  speak  of  sense- 
memory  when  the  phantasms  are  closely  allied  in  char- 
acter to  objects  seen  before,  of  hallucinations  when  the 
phantoms  arise  more  freely  and  independently.  But 
no  sharp  distinction  between  the  two  cases  can  be 
maintained.^ 

1 1  am  acquainted  with  all  manner  of  sight-phantasms  from  my  own  ex- 
perience. The  mingling  of  phantasms  with  objects  indistinctly  seen,  the  latter 
being  partly  supplanted,  are  probably  the  most  common.  Years  ago,  while 
engrossed  with  the  study  of  pulse-tracings  and  sphygmography,  the  fine  white 
curves  on  the  dark  background  often  came  up  before  my  eyes,  in  the  evening 
or  in  the  dim  light  of  day,  with  the  full  semblance  of  reality  and  objectivity. 
Later  also,  during  work  in  physics,  I  witnessed  analogous  phenomena  of 
"sense-memory."  More  rarely,  images  of  things  which  I  have  never  seen 
before,  have  appeared  before  my  eyes  in  the  day-time.  Thus,  years  ago,  on 
a  number  of  successive  days,  a  bright  red  capillary  net  (similar  to  a  so-called 
enchanted  net)  shone  out  upon  the  book  in  which  I  was  reading,  or  on  my 
writing  paper,  although  I  had  never  been  occupied  with  forms  of  this  sort. 
The  sight  of  bright-colored  changing  carpet  patterns  before  falling  asleep 
was  very  familiar  to  me  in  my  youth  ;  the  phenomenon  will  still  make  its  ap- 
pearance if  I  fix  my  attention  on  it.    One  of  my  children,  likewise,  often  tells 


88  THE  ANALYSIS  OF  THE  SENSATIONS. 

When  we  withdraw  the  retina  from  the  influence 
of  outward  excitations,  and  turn  the  attention  to  the 
field  of  vision  alone,  traces  of  phantasms  are  almost 
always  present.  Indeed,  they  make  their  appearance 
when  the  outer  excitations  are  merely  weak  and  indis- 
tinct, in  a  poor  and  dull  light,  or  when  we  look,  for 
example,  at  a  surface  covered  with  dim,  blurred  spots, 
or  at  a  cloud,  or  at  a  grey  wall.  The  figures  which 
we  then  seem  to  see,  provided  they  are  not  produced 
by  a  direct  act  of  attention  in  selecting  and  combining 
distinctly  visible  spots,  are  certainly  not  products  of 
representation,  but  constitute,  at  least  in  part,  sponta- 
neous phantasms,  which,  for  the  time  being  and  at 
some  points,  take  forcible  precedence  over  the  retinal 
excitation.^ 


me  of  "  seeing  flowers  "  before  falling  asleep.  Less  often,  I  see  in  the  even- 
ing, before  falling  asleep,  manifold  human  figures,  which  alter  without  the 
action  of  my  will.  On  a  single  occasion  I  attempted  successfully  to  change  a 
human  face  into  a  fleshless  skull ;  this  solitary  instance  may,  however,  be  an 
accident.  It  has  often  happened  to  me  that,  on  awaking  in  a  dark  room, 
the  images  of  my  latest  dreams  remained  present  in  vivid  colors  and  in  ab- 
undant light.  A  peculiar  phenomenon,  which  has  for  some  years  frequently 
occurred  with  me  is  the  following.  I  awake  and  lie  motionless  with  my  eyes 
closed.  Before  me  I  see  the  bedspread  with  all  its  little  folds,  and  upon  the 
latter,  motionless  and  unchanging,  my  hands  in  all  their  details.  If  I  open 
my  eyes,  either  it  is  quite  dark,  or  it  is  light,  but  the  spread  and  my  hands  He 
quite  diiferently  from  the  manner  in  which  they  appeared  to  me.  This  a  re- 
markably fixed  and  persistent  phantasm  with  me,  such  as  I  have  not  observed 
under  other  conditions. 

1  Leonardo  da  Vinci  discusses  the  mingling  of  phantasms  with  objects 
seen,  he.  cit.,  p.  56,  in  the  following  words: 

"I  shall  not  omit  to  give  a  place  among  these  directions  to  a  newly  dis- 
"  covered  sort  of  observation,  which  may,  indeed,  make  a  small  and  almost 
"  ludicrous  appearance,  but  which  is,  nevertheless,  very  useful  in  awakening 
"the  mind  to  various  discoveries.  It  consists  in  this,  that  thou  shouldst  re- 
"gard  various  walls  which  are  covered  with  all  manner  of  spots,  or  stone  of 
"  different  composition.  If  thou  hast  any  capacity  for  discovery,  thou  mayest 
"  behold  there  things  which  resemble  various  landscapes  decked  with  moun- 


RELATIONS  OF  THE  SIGHT-SENSATIONS.         89 

All  marked  and  independent  appearance  of  phan- 
tasms without  excitation  of  the  retina — dreams  and 
the  half-waking  state  excepted — must,  by  reason  of 
their  biological  purposelessness,  be  accounted  patho- 
logical. In  like  manner,  we  are  constrained  to  regard 
every  abnormal  dependence  of  phantasms  upon  the 
will  as  pathological.  Such,  very  likely,  are  the  states 
that  occur  in  insane  persons  who  regard  themselves  as 
very  powerful,  as  God,  etc. 


After  these  introductory  considerations  we  may 
now  turn  to  the  consideration  of  a  few  physiologico- 
optical  phenomena,  the  full  explanation  of  which,  it  is 
true,  is  still  distant,  but  which  are  best  understood  as 
the  expressions  of  an  independent  life  on  the  part  of 
the  sense-organs. 

"  tains,  rivers,  cliffs,  trees,  large  plains,  hills  and  valleys  of  many  a  sort.  Thou 
"canst  also  behold  all  manner  of  battles,  life-like  positions  of  strange,  un- 
"  familiar  figures,  expressions  of  face,  costumes,  and  numberless  things 
"which  thou  mayest  put  into  good  and  perfect  form.  The  experience  with 
"  regard  to  walls  and  stone  of  this  sort  is  similar  to  that  of  the  ringing  of 
"bells,  in  the  strokes  of  which  thou  willst  find  anew  every  name  and  every 
"word  that  thou  mayest  imagine  to  thyself. 

"Do  not  despise  this  opinion  of  mine  when  I  counsel  thee  sometimes  to 
"pause  and  look  at  the  spots  on  walls,  or  the  ashes  in  the  fire,  or  the  clouds, 
"or  mud,  or  other  places;  thou  willst  make  very  wonderful  discoveries  in 
"them,  if  thou  observest  them  rightly.  For  the  mind  of  the  painter  is  stim- 
"  ulated  by  them  to  many  new  discoveries,  be  it  in  the  composition  of  battles, 
"of  animals  and  human  beings,  or  in  various  compositions  of  landscapes, 
"and  of  monstrous  things,  as  devils  and  the  like,  which  are  calculated  to 
"bring  thee  honor.  That  is,  through  confused  and  undefined  things  the  mind 
"is  awakened  to  new  discoveries.  But  take  heed,  first,  that  thou  understand- 
"est  how  to  shape  well  all  the  members  of  the  things  that  thou  wishest  to 
"represent,  for  instance,  the  limbs  of  living  beings,  as  also  the  parts  of  a 
"landscape,  namely  the  stones,  trees,  and  the  like." 


90  THE  ANALYSIS  OF  THE  SENSATIONS, 

We  usually  see  with  both  eyes,  and  agreeably  to 
definite  needs  of  life,  not  colors  and  forms,  but  bodies 
in  space.  Not  the  elements  of  the  complex,  but  the 
physiologico-optical  complex  entire^  is  of  importance. 
This  complex  the  eye  seeks  to  fill  out  and  supplement, 
according  to  the  habits  acquired  (or  inherited)  under 
its  environment,  whenever,  as  a  result  of  special  cir- 
cumstances, the  appearance  of  the  complex  is  incom- 
plete. This  occurs  oftenest  in  monocular  vision,  but 
is  also  possible  in  the  binocular  observation  of  very 
distant  objects  where  the  stereoscopic  differences  con- 
sequent upon  the  distance  of  the  eyes  from  each  other 
vanish. 

We  generally  perceive,  not  light  and  shadow,  but 
objects  in  space.  The  shading  of  bodies  is  scarcely 
noticed.  Differences  of  illumination  produce  differ- 
ences in  the  sensation  of  depth,  and  help  to  define  the 
form  of  bodies  where  the  stereoscopic  differences  are 
insufficient, — a  condition  which  is  very  noticeable  in 
the  observation  of  distant  mountains. 

Very  instructive,  in  this  relation,  is  the  image  on 
the  dull  plate  of  the  photographic  camera.  We  are 
often  astounded  at  the  brightness  of  the  lights  and  the 
depth  of  the  shadows,  which  were  not  noticed  in  the 
bodies  themselves  but  are  striking  when  brought  into 
a  single  plane.  I  remember  quite  well  that,  in  my 
childhood,  all  shading  appeared  to  me  an  unjustifiable 
disfigurement  of  drawing,  and  that  an  outline-sketch 
was  much  more  satisfactory  to  me.     It  is  likewise 


RELATIONS  OF  THE  SIGHT-SENSATIONS. 


91 


well-known  that  whole  peoples,  for  instance  the  Chi- 
nese, despite  a  well- developed  artistic  technique,  do 
not  shade  at  all,  or  shade  only  in  a  defective  manner. 
The  following  experiment,  which  I  made  many- 
years  ago,  illustrates  very  clearly  the  above-noticed 
relation  between  light-sensation  and  the  sensation  of 
depth.  We  place  a  visiting-card,  bent  cross- 
wise, before  us  on  the  desk,  so  that  its  bent 
edge  is  towards  us.  Let  the  light  fall  from 
the  left.  The  half  abdeis  then  much  lighter, 
the  half  beef  much  darker — a  fact  which 
is,  however,  scarcely  perceived  in  unprej- 
udiced observation.  We  now  close  one  eye.  Here- 
upon, part  of  the  space-sensations  disappear.  Still 
we  see  the  bent  card  in  space  and  nothing  noticeable 
in  the  illumination.  But  as 
soon  as  we  succeed  in  see- 
ing the  bent  edge  depressed 
instead  of  raised,  the  light 
and  the  shade  stand  out  as 
if  painted  thereon.  Such 
an  inversion  is  possible,  be- 
cause depth  is  not  deter- 
mined in  monocular  vision. 
If  in  Fig.  25,  1  O  represents  the  eye,  abe  di  section  of 
a  bent  card,  and  the  arrow  the  direction  of  the  light, 
ab  will  appear  lighter  than  be.  Also  in  2,  ab  will  ap- 
pear lighter  than  be.  Plainly,  the  eye  must  acquire 
the  habit  of  interchanging  the  illumination  of  the  sur- 


Fig.  25. 


93  THE  ANALYSIS  OF  THE  SENSATIONS. 

face-elements  and  the  fall  of  the  depth-sensation.  The 
fall  and  the  depth  diminish,  with  diminishing  illumina- 
tion, towards  the  right,  when  the  light  falls  from  the 
left  (1) ;  contrariwise,  when  it  falls  from  the  right. 
Since  the  wrappings  of  the  ball  in  which  the  retina  is 
embedded  are  translucent,  it  is  not  a  matter  of  indiffer- 
ence for  the  distribution  of  light  upon  the  retina 
whether  the  light  falls  from  the  right  or  the  left.  Ac- 
cordingly, things  are  so  arranged  that,  without  any 
aid  of  judgment,  a  fixed  habit  of  the  eye  is  developed, 
by  means  of  which  illumination  and  depth  are  def- 
initely connected.  If,  by  virtue  of  another  habit  then, 
it  is  possible  to  bring  a  part  of  the  retina  into  conflict 
with  the  first  habit,  as  in  the  above  experiment,  the 
effect  is  made  manifest  by  remarkable  sensations. 

The  purpose  of  the  preceding  remarks  is  merely  to 
point  out  the  character  of  the  phenomenon  under  con- 
sideration and  to  indicate  the  direction  in  which  a 
physiological  explanation  (exclusive  of  psychological 
speculation)  is  to  be  sought.  We  will  further  remark 
that,  with  respect  to  interchangeable  qualities  of  sen- 
sation, a  principle  similar  to  that  of  the  conservation 
of  energy  seems  to  hold.  Differences  of  illumination 
are  partly  transformed  into  differences  of  perspective 
depth,  and  in  this  transformation  are  weakened  in  their 
first  capacity.  At  the  expense  of  differences  of  depth, 
on  the  other  hand,  differences  of  illumination  may  be 
augmented.  An  analogous  observation  will  be  made 
later  on  in  another  connexion. 


RELATIONS  OF  THE  SIGHT-SENSATIONS.         93 

5- 
The  habit  of  observing  bodies  as  such,  that  is,  of 
giving  attention  to  a  large  and  spatially  cohering  mass 
of  light-sensations,  carries  within  it  a  source  of  pe- 
culiar and  ever  astonishing  phenomena.  A  two-colored 
painting  or  drawing,  for  instance,  appears  in  general 
quite  different  according  as  we  take  the  one  or  the 
other  color  as  the  background.  The  puzzle  pictures,  in 
which,  for  example,  an  ap- 
parition makes  its  appear- 
ance between  tree-trunks  as 
soon  as  the  dark  trees  are 
taken  as  the  background, 
and  the  bright  sky  as  the 
object,  are  well  known.  In 
exceptional  instances  only 
do  background  and  object 
possess  the  same  form — 
a  configuration  frequently 
employed  in  ornamental  de- 
signs, as  may  be  seen  in  tig.  a6. 
Fig.  26,  taken  from  page  15  of  the  afore-mentioned 
Grammar  of  Orna?nent,  also  in  Figs.  20  and  22  of  Plate 
35,  and  in  Fig.  13  of  Plate  43  of  that  work. 

6. 

The  phenomena  of  space-vision  which  accompany 
the  monocular  observation  of  a  perspective  drawing, 


94  THE  ANALYSIS  OF  THE  SENSATIONS. 

or,  what  amounts  to  the  same  thing,  the  monocular 
observation  of  a  spatial  object,  are  generally  very 
lightly  passed  over,  as  being  self-evident  in  nature. 
But  I  am  of  the  opinion  that  there  is  yet  much  to  be 
investigated  in  these  phenomena.  One  and  the  same 
perspective  drawing  may  represent  an  unlimited  num- 
ber of  different  objects,  and  consequently  the  space- 
sensation  can  be  only  in  part  determined  by  such  a 
drawing.  If,  therefore,  despite  the  many  bodies  con- 
ceivable as  belonging  to  the  figure,  only  a  few  are 
really  seen  with  the  full  character  of  objectivity,  there 
must  exist  some  good  reason  for  the  coincidence.  It 
cannot  arise  from  the  adducing  of  auxiliary  consider- 
ations in  thought,  nor  from  the  awakening  of  conscious 
remembrances  in  any  form,  but  must  depend  on  cer- 
tain organic  habitudes  of  the  visual  sense. 

If  the  visual  sense  acts  in  conformity  with  the  hab- 
its which  it  has  acquired  through  adaptation  to  the 
life-conditions  of  the  species  and  the  individual,  we 
may,  in  the  first  place,  assume  that  it  proceeds  ac- 
cording to  the  principle  of  Probability ;  that  is,  those 
functions  which  have  been  most  frequently  excited  to- 
gether before,  will  afterwards  tend  to  make  their  ap- 
pearance together  when  only  one  is  excited.  For  ex- 
ample, those  particular  sensations  of  depth  which  in 
the  past  have  been  most  frequently  associated  with  a 
given  perspective  figure,  will  be  extremely  likely  to 
reproduce  themselves  again  when  that  figure  makes 
its  appearance,  although  not  necessarily  co-determined 


RELATIONS  OF  THE  SIGHT-SENSATIONS.        95 

thereby.  Furthermore,  a  principle  of  economy  ap- 
pears to  manifest  itself  in  the  observation  of  perspec- 
tive drawings ;  that  is  to  say,  the  visual  sense  never 
of  itself  puts  forth  greater  efforts  than  are  demanded 
by  the  excitation.  The  two  principles  coincide  in  their 
results,  as  we  shall  presently  see. 


7. 

The  following  may  serve  as  a  detailed  illustration 
of  the  above.  When  we  look  at  a  straight  line  in  a 
perspective  drawing,  we  always  see  it  as  a  straight 
line  in  space,  although  the  straight  line  as  a  perspec- 
tive drawing  may  correspond  to  an  unlimited  number 
of  different  plane  spatial  curves.  But  only  in  the  spe- 
cial case  where  the  plane  of  a  curve  passes  through 
the  centre  of  one  eye,  will  it  be  delineated  on  the  retina 
in  question  as  a  straight  line  (or  as  a  great  circle),  and 
only  in  the  yet  more  special  case  where  the  plane  of 
the  curve  passes  through  the  centres  of  both  eyes,  will 
it  be  delineated  on  both  as  a  straight  line.  It  is  thus 
extremely  improbable  that  a  plane  curve  should  ever 
appear  a  straight  line,  while  on  the  other  hand  a 
straight  line  in  space  is  always  reflected  upon  both 
retinas  as  a  straight  line.  The  most  probable  object, 
therefore,  answering  to  a  perspective  straight  line,  is 
a  spatial  straight  line. 

The  straight  line  has  various  geometrical  proper- 
ties. But  these  geometrical  properties,  for  example  the 


96  THE  ANALYSIS  OF  THE  SENSATIONS, 

familiar  characteristic  of  being  the  shortest  distance  be- 
tween two  points,  are  not  physiologically  of  importance. 
It  is  of  far  more  consequence  that  straight  lines  lying 
in  the  median  plane  or  perpendicular  thereto  are  phy- 
siologically symmetrical  to  themselves.  A  vertical 
lying  in  the  median  plane  is  also  physiologically  dis- 
tinguished by  its  perfect  uniformity  of  depth-sensa- 
tion, and  by  its  coincidence  with  the  direction  of  grav- 
ity. All  vertical  straight  lines  may  be  readily  and 
quickly  made  to  coincide  with  the  median  plane,  and 
consequently  partake  of  this  physiological  advantage. 
But  the  spatial  straight  line  generally ^  must  be  physio- 
logically distinguished  by  some  different  mark.  Its 
sameness  of  direction  in  all  its  elements  has  already 
been  pointed  out.  In  addition  to  this,  however,  it  is 
to  be  noted  that  every  point  of  a  straight  line  in  space 
marks  the  mean  of  the  depth-sensations  of  the  neigh- 
boring points.  Thus  the  straight  line  in  space  repre- 
sents a  minimum  of  departure  from  the  mean  of  the  depth- 
sensations  ;  and  the  assumption  forthwith  presents 
itself  that  the  straight  line  is  seen  with  the  least  effort. 
The  visual  sense  acts  therefore  in  conformity  with  the 
principle  of  economy,  and,  at  the  same  time,  in  con- 
formity with  the  principle  of  probability,  when  it  ex- 
hibits a  preference  for  straight  lines.* 

1  As  early  as  1866,  I  wrote,  in  the  Proceedings  of  the  Vienna  Academy,  Vol. 
54 :  "  Sino*  straight  lines  everywhere  surround  civilised  human  beings,  we 
may,  I  think,  assume,  that  every  straight  line  which  can  possibly  be  produced 
upon  the  retina  has  been  seen  numberless  times,  in  every  possible  way,  spa- 
tially as  a  straight  line.  The  efficiency  of  the  eye  in  the  interpretation  of 
■traigbt  lines  ought  not,  therefore,  to  astonish  us."    £ven  then  I  wrote  this 


RELATIONS  OF  THE  SIGHT-SENSATIONS,        97 

8. 

The  deviation  of  a  sensation  from  the  mean  of  the 
adjacent  sensations  is  always  noticeable,  and  exacts 
a  special  effort  on  the  part  of  the  sense-organ.  Every 
new  turn  of  a  curve,  every  projection  or  depression  of 
a  surface,  involves  a  deviation  of  some  space-sensa- 
tion from  the  mean  of  the  surrounding  field  on  which 
the  attention  is  directed.  The  plane  is  distinguished 
physiologically  by  the  fact  that  this  deviation  from 
the  mean  is  a  minimum,  or  for  each  point  in  particu- 
lar =  0.  In  looking  through  a  stereoscope  at  a  spotted 
surface,  the  separate  images  of  which  have  not  yet 
been  combined  into  a  binocular  view,  we  experience 
a  peculiarly  agreeable  impression  when  the  whole  is 
suddenly  flattened  out  into  a  plane.  The  aesthetic  im- 
pressions produced  by  the  circle  and  the  sphere  seem 
to  have  their  source  mainly  in  the  fact  that  the  above- 
mentioned  deviation  from  the  mean  is  the  same  for  all 
points. 

That  the  deviation  from  the  mean  of  adjacent  parts 
plays  a  role  in  light-sensation  I  pointed  out  many 
years  ago.^     If  a  row  of  black  and  white  sectors,  such 

passage  (opposing  the  Darwinian  view,  which  I  supported  in  the  same  paper) 
half-heartedly.  To-day  1  am  more  than  ever  convinced  that  the  efficiency 
referred  to  is  not  the  result  of  individual  functioning,  nor  indeed  of  human 
functioning,  but  that  it  is  also  characteristic  of  animals,  and  is,  at  least  in 
part,  a  matter  of  inheritance. 

1 "  Ueber  die  Wirkung  der  raumlichen  Vertheilung  des  Lichtreizes  auf 
die  Netzhaut."  Sitzztngsbcrichte  der  Wiener  Akadevtie  (1865),  Vol.  52.  Con- 
tinuation of  the  same  inquiry  :  Sitzber.  (1866),  Vol.  54;  Sitzber.  (1868),  Vol.  57; 
Vierteljahrsschrtft  fur  Psychiatrie,  Neuwied-Leip«ig,  1868,  ("  Ueber  die  Ab- 
hangigkeit  der  Netzhautstellen  von  einander  "). 


98  THE  ANALYSIS  OF  THE  SENSATIONS. 

as  are  shown  in  Fig.  27,  be  painted  on  a  strip  of 
paper  A  A  BB,  and  this  be  then  wrapped  about  a  cyl- 
inder the  axis  o£  which  is  parallel  to  AB^  there  will  be 
produced,  on  the  rapid  rotation  of  the  latter,  a  grey- 
field  with  increasing  illumination  from  B  to  Ay  in 
which,  however,  a  bright  line  a  a,  and  a  dark  line 
P  ft,  make  their  appearance.  The  points  which  corre- 
spond to  the  indentations  a  are  not  physically  brighter 
than  the  neighboring  parts,  but  their  light-intensity 


Fig.  37. 

exceeds  the  mean  intensity  of  the  immediately  adja- 
cent parts,  while,  on  the  other  hand,  the  light-intensity 
at  ft  falls  short  of  the  mean  intensity  of  the  adjacent 
parts.*  This  deviation  from  the  mean  is  distinctly 
felt,  and  accordingly  imposes  a  special  burden  upon 
the  organ  of  sight.  Of  what  significance  this  circum- 
stance is  for  saliency  and  the  sharp  spatial  definition 
of  objects,  I  pointed  out  long  ago. 

1 A  remark  concerning  the  analogies  between  light-sensation  and  the  po- 
tential function  will  be  found  in  my  note  "Concerning  Mr.  Gu^bhard's  Rep- 
resentation of  Equipotential  Curves,"  IViedemann't  Annaltn  (i88a),  Vol 
XVII.,  p.  864. 


RELATIONS  OF  THE  SIGHT-SENSATIONS,         99 


With  regard  to  the  depth-sensation  excited  by  a 
drawing  viewed  monocularly,  the  following  experi- 
ments are  instructive.  Fig.  28  is  a  plane  quadrilateral 
with  its  two  diagonals.  If  we  regard  it  monocularly, 
it  is  most  easily  seen,  according  to  the  law  of  prob- 
ability, as  a  plane.  In  the  great  majority  of  cases, 
objects  which  are  not  plane, /^r^^  the  eye  to  the  vision 
of  depth.  Where  this  compulsion  is 
lacking,  the  plane  object  is  the  most 
probable  and  at  the  same  time  the  easi- 
est for  the  organ  of  sight. 

The  same  drawing  may  be  also 
viewed  monocularly  as  a  tetrahedron, 
the  edge  bd  oi  which  lies  in  front  of 
ac^  or  as  a  tetrahedron,  the  edge  bd  oi  which  lies 
back  of  ac.  The  influence  of  the  imagination  and  the 
will  upon  the  visual  process  is  extremely  limited ;  it 
is  restricted  to  the  directing  of  the  attention  and  to 
the  select  ion  of  the  appropriate  disposition  of  the  organ 
of  sight  for  one  of  a  number  of  cases  given  by  habit, 
of  which,  however,  each  one,  when  chosen,  runs  its 
course  with  mechanical  certainty  and  precision.  Look- 
ing at  the  point  <f,  we  can,  as  a  fact,  produce  either 
of  the  two  optically  possible  tetrahedrons  at  will,  ac- 
cording as  we  represent  to  ourselves  bd  nearer  or  far- 
ther away  than  ac.     The  organ  of  sight  is  practised  in 


loo  THE  ANALYSIS  OF  THE  SENSATIONS. 

the  representation  of  these  two  cases,  since  it  often 
happens  that  one  body  is  partly  concealed  by  another. 

The  same  figure  may,  finally,  be  seen  as  a  four- 
sided  pyramid,  if  we  imagine  the  conspicuously  situ- 
ated point  of  intersection  e  before  or  behind  the  plane 
abed.  This  is  difficult  to  do,  if  <^^^and  aec  are  two 
perfectly  straight  lines,  because  it  conflicts  with  the 
habit  of  the  organ  of  sight  to  see,  without  constraint, 
a  straight  line  bent ;  the  effort  is  successful  only  be- 
cause the  point  e  has  a  conspicuous  position.  But  if 
there  is  a  slight  indentation  at  <f,  the  attempt  involves 
no  difficulty. 

The  effect  of  a  linear  perspective  drawing  is  felt  as 
unerringly  by  one  who  is  ignorant  of  perspective  as  by 
one  who  is  thoroughly  conversant  with  the  theory, 
provided  the  former  is  able  to  disregard  the  plane  of 
the  drawing, — a  condition  readily  fulfilled  in  monoc- 
ular observation.  Reflexion,  and  even  the  remem- 
brance of  seen  objects,  have,  according  to  my  belief, 
little  or  nothing  to  do  with  the  effect  in  question. 
Why  the  straight  lines  of  a  drawing  are  seen  as  spa- 
tial straight  lines,  has  already  been  pointed  out. 
Where  straight  lines  appear  to  converge  to  a  point  in 
the  plane  of  the  drawing,  the  converging  or  approach- 
ing ends  are  referred,  according  to  the  principle  of 
probability  and  economy,  to  like  or  to  nearly  like 
depth.  Herewith  we  have  the  effect  of  the  vanishing 
points.  Such  lines  may  be  seen  parallel,  but  there  is 
no  necessity  for  such  an  impression.     If  we  hold  the 


RELATIONS  OF  THE  SIGHT-SENSATIONS.       loi 


Fig.  29. 


drawing,  Fig.  29,  on  a  level  with  the  eye,  it  may  rep- 
resent to  us  a  glance  down  a  passage-way.  The  ends 
ghef  are  referred  to  like  distances.  If  the  distance 
is  great,  the  lines  a  e,  bf^  eg,  dh  appear  horizontal.  If 
we  raise  the  drawing,  the  ends  efgh  rise,  and  the  floor 
abef  seems  to  have  an  upward  slope. 
Upon  lowering  the  drawing,  the  op- 
posite phenomenon  is  presented  ;  and 
analogous  changes  may  be  observed 
by  moving  the  drawing  towards  the 
right  or  the  left.  In  these  facts,  the 
elements  of  perspective  effect  find  simple  and  clear  ex- 
pression. 

Plane  drawings,  provided  they  consist  entirely  of 
straight  lines,  everywhere  intersecting  each  other  at 
right  angles,  almost  always  appear  plane.  If  oblique 
intersections  and  curved  lines  occur,  the  lines  easily 
pass  out  of  the  plane ;  as  is  shown,  for 
example,  by  Fig.  30,  which  may,  without 
difficulty,  be  conceived  as  a  curved  sheet 
of  paper.  When  outlines,  such  as  are 
represented  in  Fig.  30,  have  assumed  defi- 
nite spatial  form,  and  are  seen  as  the 
boundary  of  a  surface,  the  latter,  to  describe  it  briefly, 
appears  as  fiat  as  possible,  that  is  to  say,  is  presented 
with  a  minimum  of  deviation  from  the  mean  of  the 
depth-sensation.^ 


Fig.  30. 


IHere  again,  the  depth-sensation  resembles  the  potential  function,  in  a 
space  at  the  boundaries  of  which  it  is  determined.    This  flat-as-possible  sur 


xoa 


THE  ANALYSIS  OF  THE  SENSATIONS. 


lO. 


« 
Fig.  31. 


The  peculiar  action  of  lines  intersecting  obliquely 
in  the  plane  of  the  drawing  (or  on  the  retina),  whereby 
the  same  are  mutually  and  jointly  forced  out  of  the 
plane  of  the  drawing  (or  out  of  the  plane  perpendicu- 
a  ^     lar  to  the  line  of  sight)  was  first  observed 

by  me  on  the  occasion  of  the  above-men- 
tioned (p.  91)  experiment  with  the  monoc- 
ular inversion  of  a  card.  The  card  in  Fig. 
31,  whose  edge  be  when  turned  outwards  is 
in  a  vertical  position,  assumes,  on  my  seeing 
be  depressed,  a  recumbent  position,  like  that  of  a  book 
lying  open  upon  my  table,  with  the  result  that  b  zr^- 
pe^xs  farther  away  than  e.  When  one  is  perfectly  ac- 
quainted with  the  phenomenon,    the  inversion  may 

be  performed  with  almost 
every  object,  and  one  can 
always  observe  along  with 
the  change  of  form  (along 
with  the  flapping)  a  remark- 
able simultaneous  change 
of  position.  The  effect  is 
especially  astonishing  in  the  case  of  transparent  ob- 
jects. Let  abed  he  a  section  of  a  glass  cube  lying  on 
a  table  //,  and  let  O  be  the  eye.  (Fig.  32.)  On 
monocular  inversion,  the  angle  a  is  projected  to  a', 

face  does  not  coincide  with  the  surface  of  minimal  area,  which  would  be  ob- 
tained if  the  spatial  outlines  were  made  of  wire,  and  then  dipped  in  soap- 
suds, producing  a  liquid  film  of  Plateau. 


RELATIONS  OF  THE  SIGHT-SENSATIONS.       103 

b  to  the  nearer  point  3',  c  to  c\  and  d  to  d\  The 
cube  will  seem  to  stand  obliquely  on  its  edge  c'  upon 
the  table  /'  /'.  In  order  that  the  drawing  might  afford 
a  better  survey  of  the  phenomenon,  the  two  views 
have  been  represented  behind,  not  within  one  another. 
If  a  drinking-glass  partly  filled  with  a  colored  liquid 
be  substituted  for  the  cube,  it  will  be  seen,  together 
with  the  surface  of  the  liquid,  in  a  similar  oblique  po- 
sition. 

With  sufficient  attention,  the  same  phenomena 
may  be  provoked  in  any  linear  drawing.  If  we  place 
the  page  containing  Fig.  31  vertically  before  us,  and 
observe  it  monocularly,  we  shall  see  b  project  if  ^<?  be 
raised,  but  if  be  be  depressed  b  will  retreat  and  e 
will  project  and  come  nearer  to  the  observer.  It 
may  be  said,  briefly,  that  the  legs  of  acute  angles  are 
thrust  out  on  different  sides  of  the  plane  of  the  draw- 
ing, or  of  the  plane  perpendicular  to  the  line  of  sight, 
but  that  the  legs  of  obtuse  angles  are  thrust  out  on 
the  same  side.  We  may  also  say  that  all  angles  ex- 
hibit the  tendency  to  become  right  angles. 

I  was  not  long  in  discovering  that  the  phenomenon 
referred  to  differed  in  no  essential  respect  from  that 
presented  by  ZoUner's  pseudoscopy.  Although  these 
phenomena  have  been  much  studied,  no  satisfactory 
explanation  of  them  has  as  yet  been  offered.  Natur- 
ally such  superficial  explanations  as,  for  instance,  the 
assumption  that  we  are  chiefly  accustomed  to  see  right 
angles,  are  inadmissible,  if  the  investigation  is  not  ut- 


104  '^'^^^  ANALYSIS  OF  771  E  SENSATIONS. 

terly  to  miscarry  or  to  be  prematurely  broken  off.  We 
see  oblique-angled  objects  often  enough,  but  never, 
without  artificial  preparation,  the  motionless,  oblique 
surface  of  a  liquid,  as  we  did  in  the  experiment  given 
above.  Yet,  the  eye,  it  would  seem,  prefers  the  oblique 
liquid  surface  to  an  oblique-angled  body. 

II. 

The  elemental  power  displayed  in  these  processes 
has,  I  believe,  its  root  in  far  simpler  habits  of  the  or- 
gan of  sight, — habits  whose  origin  doubtless  antedates 
the  civilised  life  of  man.  I  have  essayed  to  explain 
the  phenomena  in  question  by  a  contrast  of  directions 
analogous  to  the  contrast  of  colors,  but  without  arriv- 
ing at  a  satisfactory  result.  The  principle  of  economy 
likewise  affords  me  no  enlightenment. 

A  somewhat  greater  prospect  of  success  seems  to 
be  offered  by  the  principle  of  probability.  Let  us  con- 
ceive the  retina  as  a  perfect  sphere  and  imagine  the 
eye  fixed  upon  the  vertex  of  an  angle  a  in  space.  The 
planes  passing  through  the  centre  of  the  eye  and  the 
lines  containing  the  angle,  project  the  latter  upon  the 
retina,  describing  thereon  a  spherical  segment  having 
the  angle  A^  which  represents  the  angle  of  the  monoc- 
ular image.  An  infinite  number  of  values  for  ^,  now, 
varying  from  o°  to  i8o°,  may  correspond  to  a  constant 
value  of  Ay  as  will  be  seen  if  we  reflect  that  the  lines 
including  the  objective  angle  may  assume  every  pos- 
sible position  in  the  planes  yielding  their  projections. 


RELATIONS  OF  THE  SIGHT-SENSATIONS.       105 

Consequently,  to  a  seen  angle  A  we  may  have  corre- 
sponding, all  the  possible  values  of  the  objective  angle 
a  that  can  be  obtained  by  causing  each  of  the  sides, 
b  and  c,  of  the  triangle  to  vary  between  0°  and  180®. 
The  result  is,  supposing  the  calculation  to 
be  performed  in  a  definite  manner,  that  larger 
angles  are  the  most  probable  objects  cor- 
responding to  observed  acute  angles,  and 
smaller  angles  the  most  likely  counterparts  of 
observed  obtuse  angles.  I  was  not,  however, 
in  a  position  to  determine  whether  the  phe- 
nomena in  question,  which  we  might  be  in- 
clined to  regard  as  geo7netrically  alike,  could  also  be 
regarded  2iS  physiologically  the  same — a  question  which 
is  both  essential  and  important.  Moreover,  the  whole 
conception  has  still  a  slightly  too  artificial  cast  for  me. 

12. 

A  plane  linear  drawing,  monocularly  observed,  fre- 
quently appears  plane.  But  if  the  angles  be  made  to 
vary  and  motion  be  introduced,  every  drawing  of  this 
sort  will  assume  a  solid  form.  We  generally  see,  then, 
a  solid  body  in  rotation,  such  as  I  have  described  on 
a  former  occasion.^  The  well-known  acoustic  figures 
of  Lissajous,  which  on  varying  their  difference  of 
phase,  appear  to  lie  on  a  revolving  cylinder,  afford  an 
excellent  example  of  the  process  in  question. 


1 "  Beobachtungen  Qber  monoculare  SiQiQO^coT^iOt"  Sitsungsierichte  tUr 
IVitner  Akademie  (1868),  Vol.  38. 


io6  THE  ANALYSIS  OF  THE  SENSATIONS. 

Here,  again,  reference  might  be  made  to  our  habit 
of  constantly  dealing  with  solid  bodies.  In  fact,  solid 
bodies  engaged  in  revolutions  and  turnings  continually 
surround  us.  Indeed,  the  whole  material  world  in 
which  we  move  is,  to  a  certain  extent,  a  continuous 
solid  body ;  and  without  the  help  of  solid  bodies  we 
could  never  attain  to  the  conception  of  geometrical 
space.  We  do  not  generally  notice  the  position  of 
the  single  points  of  a  body  in  space,  but  apprehend 
directly  its  dimensions.  Herein  lies,  for  the  unprac- 
tised, the  main  difficulty  of  drawing  a  perspective  pic- 
ture. Children,  who  are  accustomed  to  seeing  bodies 
in  their  real  dimensions,  do  not  understand  perspec- 
tive foreshortenings,  and  are  far  better  satisfied  with 
simple  contours,  with  outline-drawings.  I  can  well 
remember  this  condition  of  mind,  and  through  this 
remembrance  am  able  to  comprehend  the  drawings  of 
the  ancient  Egyptians,  who  represent  all  parts  of  the 
body  as  far  as  possible  in  their  true  dimensions,  thus 
pressing  them,  as  it  were,  into  the  plane  of  the  draw- 
ing, as  plants  are  pressed  in  a  herbarium.  In  the  fres- 
coes of  the  Pompeians,  too,  we  still  meet  with  a  per- 
ceptible disinclination  to  foreshortening,  although 
here  the  sense  of  perspective  is  already  manifest.  The 
ancient  Italians,  on  the  other  hand,  in  the  conscious- 
ness of  their  perfect  mastery  of  the  subject,  often 
amuse  themselves  with  excessive  and  sometimes  even 
unbeautiful  foreshortenings,  which  occasionally  de- 
mand of  the  eye  considerable  exertion. 


RELATIONS  OF  THE  SIGHT-SENSATIONS,       107 

13- 
There  can  be  no  question,  therefore,  but  the  see- 
ing of  solid  bodies  with  the  distances  between  their 
salient  points  unchanged  is  much  easier  to  us  through 
habit  than  is  the  elimination  of  the  marks  of  solidity, 
which  is  always  the  result,  in  the  first  place,  of  de- 
liberate analysis.  Accordingly,  we  may  expect  that 
wherever  a  coherent  mass,  which  from  its  common 
coloring  is  apprehended  as  a  unit,  exhibits  spatial  al- 
teration, the  altering  process  will  be  seen  preferably 
as  the  motion  of  a  solid  body.  I  must  confess,  how- 
ever, that  this  conception  is  little  satisfactory  to  me. 
I  believe,  rather,  that  here,  too,  an  elemental  habit  of 
the  organ  of  sight  is  at  the  root  of  the  matter, — a  habit 
which  was  not  originally  acquired  by  the  conscious 
experience  of  the  individual,  but,  on  the  contrary, 
antecedently  facilitated  our  apprehension  of  the  move- 
ments of  solid  bodies.  If  we  should  assume,  for  ex- 
ample, that  every  diminution  of  the  transverse  dimen- 
sion of  an  optical  sensation-mass  to  which  the  atten- 
tion was  directed  had  the  tendency  to  induce  a  cor- 
responding augmentation  of  the  dimension  of  depth, 
and  vice  versa,  we  should  have  a  process  quite  anal- 
ogous to  that  which  we  have  already  considered  above 
and  which  was  compared  to  the  conservation  of  en- 
ergy. This  view  is  certainly  much  simpler  and  sup- 
plies an  adequate  explanation.  Furthermore,  it  en- 
ables us  to  comprehend  more  easily  how  so  elemental 


io8  THE  ANALYSIS  OF  THE  SENSATIONS, 

a  habit  could  be  acquired,  how  it  could  find  expressior 
in  the  organism,  and  how  the  tendency  for  the  same 
could  be  inherited. 

As  a  sort  of  counterpart  to  the  rotation  of  solid 
bodies  exhibited  to  us  by  the  organ  of  sight,  I  will 
cite  here  an  additional  observation.  If  an  egg,  or 
ellipsoid  with  dull,  uniform  surface  be  rolled  over  the 
top  of  a  table,  but  in  such  manner  that  it  does  not 
turn  about  its  axis  of  generation,  but  performs  jolting 
movements,  we  shall  fancy  we  see,  on  viewing  it  bi- 
nocularly,  a  liquid  body,  or  large  oscillating  drop.  The 
phenomenon  is  still  more  noticeable  if  the  egg,  with 
its  longitudinal  axis  in  a  horizontal  position,  be  set 
in  moderately  rapid  rotation  about  a  vertical  axis. 
This  effect  is  immediately  destroyed  when  marks, 
whose  movements  we  may  follow,  are  made  upon  the 
surface  of  the  ^g%.  A  rotating  solid  body  is  then  seen. 

The  explanations  offered  in  this  chapter  are  cer- 
tainly far  from  complete,  yet  I  believe  that  the  con- 
siderations adduced  will  have  some  effect  in  stimulat- 
ing and  preparing  the  way  for  a  more  exact  and  thor- 
ough study  of  these  phenomena. 


TIME-SENSATION. 


I. 

1\  TUCH  more  difficult  than  the  investigation  of 
-^ '-*-  space-sensation  is  that  of  time-sensation.  Many 
sensations  make  their  appearance  with,  others  with- 
out, space-sensation.  But  time-sensation  accompanies 
every  other  sensation,  and  can  be  wholly  separated 
from  none.  We  are  referred,  therefore,  in  our  in- 
vestigations here,  to  the  variations  of  time-sensation. 
With  this  psychological  difficulty  is  associated  an- 
other, consisting  of  the  fact  that  the  physiological 
processes  underlying  the  time-sensation  are  less  known, 
more  radical,  and  more  thoroughly  concealed  than  the 
processes  underlying  the  other  sensations.  Our  analy- 
sis, therefore,  must  confine  itself  chiefly  to  the  psycho- 
logical side,  without  approaching  the  question  from 
its  physical  aspect,  as  is  possible,  in  part  at  least,  in 
the  provinces  of  the  other  senses. 

IThe  position  which  I  here  take  dififers  only  slightly  from  that  of  my 
•' Untersuchungen  uber  den  Zeitsinn  des  Ohres,"  Sitzber.  d.  Wiener  Akade- 
mie,  Vol.  51,  1865.  Into  the  details  of  these  earlier  experiments,  begun  in  i860, 
I  shall  not  enter  again  here. 


no  THE  ANALYSIS  OF  THE  SENSATIONS, 

2. 

That  a  definite,  specific  time-sensation  exists,  ap- 
pears to  me  beyond  all  doubt.  The  rhythmical  iden- 
tity of  the  two  adjoined  measures,  which  vary  utterly 


k^in  i>\f  ^fi 


in  the  order  of  their  tones,  is  immediately  recognised. 
We  have  not  to  do  here  with  a  matter  of  the  under- 
standing or  of  reflexion,  but  with  one  of  sensation. 
In  the  same  manner  that  bodies  of  different  colors 
may  possess  the  same  spatial  form,  so  here  we  have 
two  tonal  entities  which,  acoustically,  are  differently 
colored,  but  possess  the  same  temporal  form.  As  in 
the  one  case  we  pick  out  by  an  immediate  act  of 
feeling  the  identical  spatial  components,  so  here  we 
immediately  detect  the  identical  temporal  components, 
or  the  sameness  of  the  rhythm. 

3. 

On  hearing  a  number  of  strokes  of  a  bell,  which 
are  exactly  alike  acoustically,  I  discriminate  between 
the  first,  second,  third,  and  so  on.  Do  the  accompany- 
ing thoughts,  perhaps,  or  other  accidental  sensations, 
with  which  the  strokes  of  the  bell  happen  to  be  asso- 
ciated, afford  these  distinguishing  marks  ?  I  do  not 
believe  that  any  one  will  seriously  uphold  this  view. 
How  uncertain  and  unreliable  would  our  estimate  of 
time  prove  in  such  an  event !    What  would  become  of 


TJME-SENSATION.  iii 

it  if  that  accidental  background  of  thought  and  sensa- 
tion should  suddenly  vanish  from  memory  ? 

While  I  am  reflecting  upon  something,  the  clock 
strikes,  but  I  give  no  heed  to  it.  After  it  has  finished 
striking,  it  may  be  of  importance  to  me  to  count  the 
strokes.  And  as  a  fact,  there  arise  in  my  memory  dis- 
tinctly one,  two,  three,  four  strokes.  I  give  here  my 
whole  attention  to  this  recollection,  and  by  this  means 
the  subject  on  which  I  was  reflecting  during  the  striking 
of  the  clock,  for  the  moment  completely  vanishes  from 
me.  The  supposed  background  against  which  I  could 
note  the  strokes  of  the  bell,  is  now  wanting  to  me. 
By  what  mark,  then,  do  I  distinguish  the  second  stroke 
from  the  first  ?  Why  do  I  not  regard  all  the  strokes, 
which  in  other  respects  are  identical,  as  one  ?  Because 
each  is  connected  for  me  with  a  special  time-sensation 
which  starts  up  into  consciousness  along  with  it.  In 
like  manner,  I  distinguish  an  image  present  in  my 
memory  from  a  creation  of  fancy  by  a  specific  time- 
sensation  different  from  that  of  the  present  moment. 

4- 

Since,  so  long  as  we  are  conscious,  time-sensation 
is  always  present,  it  is  probable  that  it  is  connected 
with  the  organic  consumption  necessarily  associated 
with  consciousness, — that  we  feel  the  work  of  attention 
as  time.  During  severe  effort  of  attention  time  is  long 
to  us,  during  easy  employment  short.  In  phlegmatic 
conditions,  when  we  scarcely  notice  our  surroundings^ 


ZZ2  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

the  hours  pass  rapidly  away.  When  our  attention  is 
completely  exhausted,  we  sleep.  In  dreamless  sleep, 
the  sensation  of  time  is  lacking.  When  profound  sleep 
intervenes,  yesterday  is  connected  with  to-day  only  by 
an  intellectual  bond. 

The  fatiguing  of  the  organ  of  consciousness  goes 
on  continually  in  waking  hours,  and  the  labor  of  at- 
tention increases  just  as  continually.  The  sensations 
connected  with  greater  expenditure  of  attention  ap- 
pear to  us  to  happen  later. 

Normal  as  well  as  abnormal  psychical  acts  appear 
to  accord  with  this  conception.  Since  the  attention 
cannot  be  fixed  upon  two  different  sense-organs  at 
once,  the  sensations  of  two  organs  can  never  occur  to- 
gether and  yet  be  accompanied  by  an  absolutely  equiva- 
lent effort  of  attention.  Seemingly,  therefore,  the  one 
occurs  later  than  the  other.  A  parallel  of  this  so- 
called  personal  equation  of  astronomers,  having  its 
ground  in  analogous  facts,  is  also  frequently  observed 
in  the  same  sense-province.  It  is  a  well-known  fact 
that  an  optical  impression  which  arises  physically 
later  may  yet,  under  certain  circumstances,  appear  to 
occur  earlier.  It  sometimes  happens,  for  example, 
that  a  surgeon,  in  bleeding,  first  sees  the  blood  burst 
forth  and  afterwards  his  lancet  enter.  ^  Dvorak  has 
shown,'  in  a  series  of  experiments  which  he  carried 

1  Compare  Fechner,  i^cAo/A^ftV^.    Leipsic,  i860.    Vol.  II.,  p.  433. 

2  Dvorak,  "  Ueber  Analoga  der  persOnlichen  Differenz  zwiscben  beiden 
Augen  und  den  Netzhautstellen  desselben  Auges."  Sitzber.  d.  kdnigl.  bohm. 
G«uU*cht^ft  dmr  WisMnseha/ttn,  {Matk.-naturvt.  Cl»*M),  von  8.  Marz,  1872. 


TIME-SENS  A  TION. 


113 


red 


out  at  my  desire,  years  ago,  that  this  relation  may  be 
produced  at  will,  the  object  on  which  the  attention  is 
centred  appearing  (even  in  the  case  of  an  actual  tar- 
diness of  1/8-1/6  of  a  second)  earlier  than  that  indi- 
rectly seen.  It  is  quite  possible  that  the  familiar  ex- 
perience of  the  surgeon  may  find  its  explanation  in 
this  fact.  The  time  which  the  attention  requires  to 
turn  from  one  place  at  which  it  is  occupied,  to  an- 
other, is  shown  in  the  following  experiment  instituted 
by  me.^  Two  bright  red  squares  measuring  two  centi- 
metres across  and  situated  on 
a  black  background  eight  cen- 
timetres apart,  are  illuminated 
in  a  perfectly  dark  room  by  an 
electric  spark  concealed  from 
the  eye.  The  square  directly 
seen  appears  red,  but  that 
indirectly  seen  appears  green, — and  often  quite  in- 
tensely so.  The  tardy  attention  finds  the  indirectly 
seen  square  when  it  is  already  in  the  stage  of  Purkinje's 
positive  after-image.  A  Geissler's  tube  with  two  bright 
red  spots  at  a  short  distance  from  one  another,  exhib- 
its, on  the  passage  of  a  single  discharge,  the  same 
phenomenon. 


red 

red 

indir.  seen  dir.  seea 

Fig.  34- 


The   following   interesting   experience   should  be 
cited  here.   Frequently  I  have  been  sitting  in  my  room, 

1  Communicated  by  Dvorak,  loc.  cit. 


XI4  THE  ANALYSIS  OF  THE  SENSATIONS. 

absorbed  in  work,  while  in  an  adjacent  room  experi- 
ments in  explosions  were  being  carried  on.  It  regu- 
larly occurred  that  I  shrank  back  startled,  before  I 
heard  the  report. 

Since  the  attention  is  especially  inert  in  dreams, 
naturally  the  most  peculiar  anachronisms  occur  in  this 
state,  as  every  one  has  doubtless  observed.  For  in- 
stance, we  dream  of  a  man  who  rushes  at  us  with  a 
revolver  and  shoots,  awake  suddenly,  and  perceive 
the  object  which,  by  its  fall,  has  produced  the  entire 
dream.  Now  there  is  nothing  absurd  in  assuming 
that  the  acoustic  excitation  enters  simultaneously  dif- 
ferent nerve-tracks  and  is  met  there  by  the  attention 
in  some  inverted  order,  just  as,  in  the  case  above 
mentioned,  I  perceived  first  the  general  disturbance 
of  the  organism  and  afterwards  the  report  of  the  ex- 
plosion. But  in  many  cases  it  is  undoubtedly  sufficient 
to  assume  the  introduction  of  sensations  into  the  frame- 
work of  a  dream  already  present. 


If  time-sensation  is  conditioned  by  progressive  or- 
ganic consumption^  or  by  the  corresponding  steady 

I  If  the  consumption,  or,  for  that  matter,  the  accumulation  of  a  "fatigue- 
material  "  were  immediately  felt,  we  might  logically  expect  a  reversion  of 
time  in  dreams.  The  eccentricities  of  dreams  may  all  be  accounted  for  by 
the  fact  that  some  sensations  and  representations  do  not  enter  consciousness 
at  all,  while  others  enter  with  too  much  difiBculty  and  too  late.  The  intellect 
often  sleeps  only  in  part.  We  converse  very  sensibly,  in  dreams,  with  per- 
sons long  deceased,  but  with  no  recollection  of  their  death.  We  reflect,  in 
the  dream-state,  concerning  dreams,  recognise  them  as  such  by  their  eccen- 
tricities, but  are  immediately  pacified  again.  I  once  dreamed  very  vividly  of 
a  mill.    The  water  flowed  downwards,  in  a  sloping  channel,  away  from  the 


TIME- SENSATION,  115 

increase  of  the  effort  following  upon  attention,  then  it 
is  intelligible  why  physiological  time  is  not  reversible 
but  moves  only  in  one  direction.  As  long  as  we  are 
in  the  waking  state  consumption  and  the  labor  of  at- 
tention can  only  increase,  not  diminish.  The  two  ac- 
companying bars  of  music,  ^ — .       ^ — ^ 

8  S 

which  present  a  symmetry  P  T  f  T  f  f  t  f  f  f 
to  the  eye  and  to  the  under-  ^^ 

standing,  show  nothing  of  the  sort  as  regards  the  sen- 
sation of  time.  In  the  province  of  rhythm,  and  of 
time  in  general,  there  is  no  symmetry. 


It  is  a  perfectly  natural,  though  somewhat  imper- 
fect conception,  to  regard  the  organ  of  consciousness 
as  capable,  in  a  weakened  degree,  of  a//  the  specific 
energies,  of  which  each  sense-organ  is  capable  only  of 
a.  few.  Hence  the  shadowy  and  evanescent  character 
of  representation  as  compared  with  sensation,  through 
which  it  must  be  constantly  nourished  and  revivified. 

mill,  and  hard  by,  in  just  such  another  channel,  upwards  to  the  mill.  I  vras 
not  at  all  disturbed  by  the  contradiction.— At  a  time  when  much  engrossed 
with  the  subject  of  space-sensation,  I  dreamed  of  a  walk  in  the  woods.  Sud- 
denly I  noticed  the  defective  perspective  displacement  of  the  trees,  and  by 
this  recognised  that  I  was  dreaming.  The  missing  displacements,  however, 
were  immediately  supplied. — Again,  while  dreaming,  I  saw  in  my  laboratory 
a  beaker  filled  with  water,  in  which  a  candle  was  serenely  burning.  "  Where 
does  it  get  its  oxygen  from  ?  "  I  thought.  "  It  is  absorbed  in  the  water,"  was 
the  answer.  "Where  do  the  gases  produced  in  the  combustion  go  to?" 
The  bubbles  from  the  flame,  mounted  upwards  in  the  water,  and  I  was  satis- 
fied. 

[Remarkable  observations  concerning  dreams,  which  I  have  frequently 
verified  in  my  own  personal  experience,  may  be  found  in  a  book  published  by 
W.  Robert,  entitled  Der  Traum  ah  Naturnothwendigkeit  (Hamburg:  Her. 
mann  Seippel.    1886).— Mach,  1895.] 


xi6  THE  ANALYSIS  OF  THE  SENSATIONS. 

Hence  also  the  capacity  of  consciousness  to  serve  as  a 
bridge  of  communication  between  all  sensations  and 
memories.  With  every  specific  energy  of  the  organ  of 
consciousness,  we  should  then  have  to  conceive  still 
another  particular  energy,  the  sensation  of  time,  asso- 
ciated, so  that  none  of  the  former  could  be  excited 
without  evoking  the  latter.  Should  this  new  energy 
appear  physiologically  superfluous  and  only  invented 
ad  hoCf  we  might  at  once  assign  to  it  an  important 
physiological  function.  What  if  this  energy  kept  up 
the  flow  of  blood  thdit  nourishes  the  brain-parts  in  their 
work,  guided  this  current  to  its  destination,  and  regu- 
lated it?  Our  conception  of  attention  and  of  time- 
sensation  would  then  receive  a  very  material  basis. 
The  fact  that  there  is  but  one  continuous  time,  too, 
would  become  intelligible,  since  the  partial  attention 
given  to  one  sense  is  always  drawn  from  the  total  at- 
tention, and  is  determined  by  it. 

8. 

In  listening  to  a  number  of  similar  strokes  from  a 
bell,  we  can  distinguish  each  from  the  others  and  also 
count  them  in  memory,  provided  they  are  few  in  num- 
ber. If  the  number  is  large,  however,  we  distinguish 
the  last  ones  from  one  another,  but  not  the  first.  In 
this  case,  if  we  would  not  make  a  mistake,  we  must 
efiunt  them  immediately  upon  their  being  sounded, 
that  is,  we  must  consciously  connect  with  each  stroke 
some  ordinal  symbol.    The  phenomenon  has  a  perfect 


TIME-SENS  A  TION.  1 17 

analogue  in  the  province  of  the  space-sense,  and  is  to 
be  explained  on  the  same  principle.  In  walking  for- 
wards, we  have  a  distinct  sensation  that  we  are  mov- 
ing away  from  a  starting-point,  but  the  physiological 
measure  of  this  removal  is  not  proportional  to  the  geo- 
metrical. In  the  same  manner,  elapsed  physiological 
time  is  subject  to  perspective  contraction,  its  single 
elements  becoming  less  and  less  distinguishable.^ 

9- 

If  a  special  time-sensation  exists,  it  goes  without 
saying  that  the  identity  of  two  rhythms  will  be  imme- 
diately recognised.  But  we  must  not  leave  the  fact 
unnoticed  that  two  rhythms  which  are  the  same  phys- 
ically may  appear  very  different  physiologically,  just 
as  the  same  space-figure  by  change  of  position  may 
give  rise  to  different  physiological  space-forms.  The 
rhythm  represented  by  the  following  notes,  for  exam- 

I  Lf  I  r  i  r  1 0*  I  r  1  r  1  l;  I  n  r  I 

12         8 

pie,  appears  quite  different  according  as  we  regard 
the  short  thick,  or  the  long  thin  vertical  lines,  or  the 
rows  of  dots,  as  the  bars.  The  reason  of  this  is  man- 
ifestly that  the  attention  (guided  by  the  accent)  is  dis- 
charged^ so  to  speak,  at  i,  2,  or  3,  that  is,  that  the 
sensations  of  time  corresponding  to  the  successive 
beats  are  compared  with  different  initial  sensations. 

1  Compare  p.  64. 


ii8  THE  ANALYSIS  OF  THE  SENSATIONS. 

The  rhythm  represented  in  the  following  diagram 
appears  physiologically  similar  to  the  preceding,  but 
only  when  similarly-marked  bars  are  taken  in  the  two 


\\i\v^^\vx\^m 


— that  is,  when  the  attention  is  introduced  at  homol- 
ogous points  of  time.  Two  physical  time-figures  may 
be  termed  similar  when  all  the  parts  of  the  one  stand 
in  the  same  relation  to  one  another  as  do  the  homol- 
ogous parts  of  the  other.  But  physiological  similarity 
makes  its  appearance  only  when  the  above  condition 
is  likewise  fulfilled.  Furthermore,  so  far  as  I  am  able 
to  judge,  we  recognise  the  identity  of  the  time-ratios 
of  two  rhythms  only  when  the  same  are  capable  of 
being  represented  by  very  small  whole  numbers.  Thus 
we  really  notice  immediately,  only  the  identity  or  non- 
identity  of  two  times,  and,  in  the  latter  case,  recog- 
nise the  ratio  of  the  two  only  by  the  fact  that  one  part 
is  exactly  contained  in  the  other.  Herewith  we  have 
an  explanation  of  the  fact  that,  in  marking  time,  the 
time  is  always  divided  into  absolutely  equal  parts. ^ 

IThe  similarity  of  space-figures  would  be  felt,  according  to  this  theory, 
much  more  immediately  than  the  similarity  of  rhythms.  The  connexion  be- 
tween rhythmic  movements  and  the  measurement  of  time,  which  probably 
has  an  important  teleological  import,  need  not  be  discussed  here. 


SENSATIONS  OF  TONE.* 


I. 


TN  tone-sensations,  also,  we  are  restricted  mainly  to 
-■-  psychological  analysis.  As  before,  the  initial  ele- 
ments of  the  investigation  are  all  we  can  offer. 

Among  the  sensations  of  tone  possessing  greatest 
importance  for  us  are  those  produced  by  the  human 
voice,  in  the  form  of  utterances  of  pleasure  and  pain, 
of  expressions  of  the  will,  and  of  the  communication 
of  thoughts  by  speech,  etc.  The  voice  and  the  organ 
of  hearing  doubtless  bear  a  close  relation  to  each  other. 
The  simplest  and  distinctest  form  in  which  sensations 
of  tone  reveal  their  remarkable  characteristics  is  music. 
Will,  feeling,  vocal  expression  and  vocal  sense-recep- 
tivity have  certainly  a  strong  physiological  connexion. 
There  is  a  good  deal  of  truth  in  the  remark  of  Schopen- 

1  Barring  details,  I  have  held  the  position  here  taken,  for  twenty  years. 
Stumpf,  to  whom  I  owe  a  debt  of  gratitude  for  the  repeated  consideration  of 
my  work,  has  many  points  of  detail  {Tonpsychologie^  Leipsic,  1883)  that  appeal 
to  me.  The  view  expressed  on  page  119  of  his  work,  however,  is  incompat- 
ible with  the  principle  of  parallelism,  my  fundamental  axiom  of  research. 
Compare  my  note,  "Zur  Analyse  der  Tonempfindungen,"  Sitzungsberichte 
der  Wiener  Akademie,  Vol.  92,  II.  Abth,,  p.  1283  (1885). 


I20  THE  ANALYSIS  OF  THE  SENSATIONS. 

hauer^  that  music  represents  the  will,  and  in  fact  gen- 
erally in  the  designation  of  music  as  a  language  of 
emotion ;  although  this  is  scarcely  the  whole  truth. 


Following  the  precedent  of  Darwin,  H.  Berg  has 
attempted  to  derive  music  from  the  amatory  cries  of 
monkeys.^  We  should  be  blind  not  to  recognise  the 
service  rendered  and  enlightenment  conveyed  by  the 
work  of  Darwin  and  Berg.  Even  at  the  present  day, 
music  has  power  to  touch  sexual  chords,  and  is,  as  a 
fact,  widely  made  use  of  in  courtship.  But  as  to  the 
question  wherein  consists  the  agreeable  quality  of 
music,  Berg  makes  no  satisfactory  answer.  And  see- 
ing that  in  the  matter  of  harmony  he  adopts  Helm- 
holtz's  position  of  the  avoidance  of  beats  and  assumes 
that  the  males  who  howled  least  disagreeably  received 
the  preference,  we  may  be  justified  in  wondering  why 
the  most  intelligent  of  these  animals  were  not  prompted 
to  maintain  silence  altogether. 

The  importance  of  tracing  the  connexion  of  a  given 
biological  phenomenon  with  the  preservation  of  the 
species,  and  of  indicating  its  phylogenetic  origin,  can- 
not be  underrated.  But  we  must  not  imagine  that  in 
having  accomplished  this  we  have  solved  all  the  prob- 
lems connected  with  the  phenomenon.  Surely  no  one 
will  think  of  explaining  the  specific  sensation  of  sexual 

1  Schopenhauer,  Die  Welt  ah  WilU  und  Vorstelhing, 
tH.  Berg,  Die  Lust  an  der  Musik.     Berlin,  1879, 


SENSATIONS  OF  TONE.  121 

pleasure  by  showing  its  connexion  with  the  preservation 
of  the  species.  We  should  be  more  likely  to  acknowl- 
edge that  the  species  is  preserved  because  the  sensa- 
tion accompanying  sexual  indulgence  is  pleasurable. 
Although  music  may  actually  remind  us  of  the  court- 
ship of  distant  progenitors,  it  must,  if  it  was  ever  used 
for  wooing,  have  contained  at  the  start  some  positive 
agreeable  quality,  which  does  not,  of  course,  preclude 
its  being  re-enforced  at  the  present  time  by  that  mem- 
ory. To  take  an  analogous  case  from  individual  life, 
the  smell  of  an  oil-lamp  which  has  just  been  extin- 
guished almost  always  agreeably  reminds  me  of  the 
magic  lantern  which  I  admired  as  a  child.  Yet  in  it- 
self the  smell  of  the  lamp  is  none  the  less  disgusting 
for  this  reason.  Nor  does  the  man  who  is  reminded, 
by  the  scent  of  roses,  of  a  pleasant  experience,  believe, 
on  this  account,  that  the  perfume  was  not  previously 
agreeable.  It  has  only  gained  by  the  association.^ 
And  if  the  view  referred  to  cannot  sufficiently  explain 
the  agreeable  quality  of  music  per  se,  it  assuredly  can 
contribute  still  less  to  the  solution  of  special  ques- 
tions, as,  for  instance,  why,  in  a  given  case,  a  fourth 
is  preferred  to  a  fifth. 


A  rather  partial  view  of  the   sensations  of  tone 
would  be  obtained  if  we  were  to  consider  only  the 


IFechner,  notably,  has  emphasised  the  significance  of  association  for 
asthetics. 


122  THE  ANALYSIS  OF  THE  SENSATIONS, 

province  of  speech  and  music.  Sensations  of  tone  are 
not  only  a  means  of  communicating  ideas,  of  express- 
ing pleasure  and  pain,  of  discriminating  between  the 
voices  of  men,  women,  and  children  ;  they  are  not 
alone  signals  of  the  exertion  or  passion  experienced 
by  the  person  speaking  or  calling ;  they  also  consti- 
tute the  means  by  which  we  distinguish  between  large 
and  small  bodies  when  sounding,  between  the  tread  of 
large  and  small  animals.  The  highest  tones,  the  very 
ones  which  the  vocal  organs  of  man  cannot  produce, 
presumably  are  of  extreme  importance  for  the  deter- 
mination of  the  direction  from  which  sounds  proceed.' 
In  fact,  it  is  more  than  likely  that  these  latter  func- 
tions of  sensations  of  tone  antedated,  in  the  animal 
world,  by  a  long  period,  those  which  merely  perform  a 
part  in  the  social  life  of  animals. 


There  is  no  one  but  will  cheerfully  acknowledge 
the  decided  advance  wrought  by  Helmholtz  in  the 
analysis  of  sensations  of  audition.'  Following  his 
principles,  we  recognise  in  noises  combinations  of  mu- 
sical sounds,  of  which  the  number,  pitch,  and  intensity 
vary  with  the  time.  In  compound  musical  sounds,  or 
clangs^  we  generally  hear,  along  with  the  fundamental 

IMach,  "  Bemerkungen  Qber  die  Function  der  Ohrmuschel"  [TrOlisch't 
Archiv/Ur  Ohrtnheilkundt ,  N.  F.,  Vol.  III.,  p.  72).— Compare  also  Mach  and 
Fischer,  "  Di«  Reflexion  und  Brechung  des  Schalles,"  Pogg.  Ann.,  Vol.  149, 
p.  421. 

S  Helmholtz,  Die  Lekrt  von  den  Tontmjfindungen,  first  edition,  Bruns- 
wick, 1863. 


SENSATIONS  OF  TONE.  123 

«,  the  partial  tones  or  harmonics  2«,  3«,  4«,  etc.,  each 
of  which  corresponds  to  simple  pendular  vibrations. 
If  two  such  musical  sounds,  the  fundamentals  of  which 
correspond  to  the  rates  of  vibration  n  and  w,  be  mel- 
odically  or  harmonically  combined,  there  may  result, 
if  certain  relations  of  n  and  m  are  satisfied,^  a  partial 
coincidence  of  the  harmonics,  whereby  in  the  first  case 
the  relationship  of  the  two  sounds  is  rendered  per- 
ceptible, and  in  the  second  a  diminution  of  beats  is 
effected.  All  this  cannot  be  disputed,  although  it  may 
not  be  deemed  exhaustive. 

We  may  also  give  our  assent  to  Helmholtz's  phys- 
iological theory  of  the  auditive  organ.  The  facts  ob- 
served on  the  simultaneous  sounding  of  simple  notes 
make  it  highly  probable  that  there  exist,  correspond- 
ing to  the  series  of  vibration-rates,  a  series  of  terminal 
nervous  organs,  so  that  for  all  the  different  rates  of 
vibration  there  are  different  sympathetic  end-organs, 
each  of  which  responds  to  only  a  few,  closely  adjacent 
rates  of  vibration.  It  is  a  question  of  lesser  importance 
whether  this  function  is  exercised  by  the  organ  of 
Corti. 

5. 

If  we  assume  with  Helmholtz  that  all  noises  admit 
of  being  resolved  into  sensations  of  tone  varying  in 
duration,  it  is  evidently  superfluous  to  seek  for  a  special 
auditive  organ  for  noises.     A  long  time  ago  (in  the 

iThe  /th  harmonic  of  n  coincides  with  the  ^th  of  m  vrhen/it  —  jm,  that 
is  m  =(^/g)  n,  where/  and  q  are  whole  numbers. 


X24  ^'^/^  ANALYSIS  OF  THE  SENSATIONS. 

winter  of  1 872-1 873)  I  took  up  the  question  of  the  re- 
lation of  noises  (especially  that  of  sharp  reports)  to 
musical  tones,  and  found  that  all  transitions  between 
the  two  may  be  observed.  A  tone  of  one  hundred  and 
twenty-eight  full  vibrations,  heard  through  a  small  ra- 
dial slit  in  a  slowly  revolving  disc,  contracts,  when  its 
duration  is  reduced  to  from  two  to  three  vibrations,  to 
a  short,  sharp  concussion  (or  weak  report)  of  very  in- 
distinct pitch,  while  with  from  four  to  five  vibrations, 
the  pitch  is  still  perfectly  distinct.  ^  On  the  other  hand, 
with  sufficient  attention,  a  pitch,  though  not  a  very 
definite  one,  may  be  detected  in  a  report  even  when  the 
latter  is  produced  by  an  aperiodic  motion  of  the  air 
(the  wave  of  an  electric  spark,  exploding  soap-bubbles 
filled  with  iH-\-0).  We  may  easily  convince  our- 
selves, furthermore,  that  in  a  piano  from  which  the 
damper  has  been  lifted,  large  exploding  bubbles  mainly 
excite  to  sympathetic  vibration  the  lower  strings,  while 
small  ones  principally  affect  the  higher  strings.  This 
fact,  it  seems  clear  to  me,  demonstrates  that  the  same 
organ  may  be  the  mediator  of  both  tone  and  noise  sen- 
sation. We  must  imagine  that  weak  aperiodic  vibra- 
tions of  the  air  having  short  durations  excite  all,  though 
preferably  the  small  dind  more  mobile  end-organs,  whilst 
the  powerful  and  more  lasting  disturbances  of  this  sort 
affect  also  the  larger  and  heavier  end-organs,  which 
from  being  less  damped  perform  vibrations  of  greater 
amplitude  and  are  thus  noticed  ;  and  furthermore  that 

1  For  fall  explanatioa  see  Appendix  II. — TVwih^ 


SENSATIONS  OF  TONE.  125 

even  in  the  case  of  comparatively  weak  periodic  vibra- 
tions of  the  air,  the  excitation,  by  an  accumulation  of 
effects,  is  manifested  in  some  definite  member  of  the 
series  of  end-organs.^  The  sensation  excited  by  a  re- 
port of  low  or  high  pitch  is  qualitatively  the  same  as 
that  produced  by  striking  at  once  a  large  number  of 
adjacent  piano-keys,  only  more  intense  and  of  shorter 
duration.  Moreover,  in  the  single  excitation  produced 
by  a  report,  the  beats  connected  with  periodic  inter- 
mittent excitations  are  eliminated. 

6. 
Yet  despite  the  recognition  with  which  the  theory 
of  Helmholtz  has  met,  there  have  not  been  wanting 
voices  which  have  called  attention  to  its  incomplete- 
ness. The  lack  of  a  positive  factor  in  the  explanation 
of  harmony  has  been  very  generally  felt,  the  mere  ab- 
sence of  beats  not  being  regarded  as  a  sufficient  and 
satisfactory  characterisation  of  harmony.  Thus  A.  v. 
Oettingen^  feels  the  want  of  some  expressed  positive 
element  characteristic  of  each  interval,  and  refuses  to 
regard  the  value  of  an  interval  as  dependent  upon  the 
physical  accident  of  the  overtones  contained  in  the 
sounds.  He  believes  that  the  positive  element  in  ques- 
tion is  to  be  found  in  the  accompanying  remembrance 

1 1  gave  an  account  of  part  of  my  experiments,  which  were  a  continuation 
of  Dvorak's  researches  on  the  after-images  due  to  variations  of  excitation 
(1870),  in  the  August  number  of  Lotos,  1873.  (See  Appendix  II.)  I  have  never 
before  mentioned  the  experiments  relative  to  the  excitement  of  piano-tones 
by  explosions.  It  will  not  be  amiss,  perhaps,  if  I  do  so  here.— Pfaundler,  S. 
Exner,  Auerbach,  BrQcke,  and  others,  subsequently  treated  the  same  question 
in  detail. 

2  Harmoniesystetn  in  dualer  Ent-wicklung  (Dorpat,  1866),  p.  3<k 


126  THE  ANALYSIS  OF  THE  SENSATIONS. 

of  the  common  fundamental  tone  (or  tonic),  as  the  har- 
monics of  which  the  composite  notes  or  clangs  of  the 
interval  have  often  occurred,  or  in  the  accompanying 
remembrance  of  the  common  overtone  (or  phonicV  be- 
longing to  the  two  (pp.  40,  47).  On  the  negative  side 
of  his  criticisms  I  am  in  complete  agreement  with  Von 
Oettingen.  But  ** remembrance"  does  not  quite  fill 
the  need  of  the  theory,  for  consonance  and  dissonance 
are  not  matters  of  representative  activity,  but  of  sen- 
sation. My  opinion,  therefore,  is  that  A.  von  Oettin- 
gen's  conception  is  physiologically  inadequate.  His 
enunciation  of  the  principle  of  duality,  however,  (or  of 
the  principle  of  the  tonic  and  phonic  relationship  of 
composite  notes),  as  also  his  conception  of  disson- 
ances as  indeterminate  composite  musical  sounds  ad- 
mitting of  more  than  one  interpretation  (p.  224)  ap- 
pear to  me  to  be  valuable  and  positive  services  to 
science.' 


1  [The  lowest  of  the  harmonics  common  to  all  I  term  the  coincident  or 
phonic  harmonic. — Von  Oettingen,  Harmoniesystem  in  dualer  Entwicklung,  p. 
3a.     Quoted  by  translator.] 

8  A  popular  statement  of  the  principle  of  duality,  of  which  Euler  [Tenta- 
men  novae  theoriae  musicae,  p.  103),  D'Alembert  {Elimens  de  mustque,  Lyons, 
1766),  and  Hauptmann  {Die  Natur  der  Harmonik  und  Metrik,  Leipsic,  1853, 
translation  by  W.  E.  Heathcote,  London,  Swan  Sonnenschein  &  Co.,  1888), 
had  all  a  faint  inkling,  is  to  be  found  in  my  Popular  Scientific  Lectures  (Chi- 
cago, 1894),  under  the  caption  "  Symmetry "  (originally  published  in  1872;. 
Perfect  symmetry,  such  as  is  found  in  the  province  of  sight,  cannot  be  imag- 
ined in  music,  since  sensations  of  tone  do  not  constitute  a  symmetrical  system. 


SENSATIONS  OF  TONE,  127 

7. 

I  myself,  as  early  as  1863^  and  also  later,'  had 
made  some  critical  remarks  on  the  theory  of  Helm- 
holtz,  and  in  1866,  in  a  small  work^  which  appeared 
shortly  before  that  of  Von  Oettingen,  very  definitely 
pointed  out  some  demands  which  a  more  perfect  the- 
ory of  the  subject  would  have  to  satisfy.  Since,  how- 
ever, up  to  the  present  time  my  remarks  have,  to  my 
knowledge,  nowhere  met  with  serious  consideration,  I 
shall  revert  to  them  here  at  length. 

8. 

We  shall  start  with  the  idea  that  a  series  of  defi- 
nitely graduated  sonant  end-organs  exists,  the  mem- 
bers of  which,  as  the  rate  of  vibration  increases,  suc- 
cessively yield  their  maximum  response,  and  we  shall 
ascribe  to  each  end-organ  its  particular  (specific)  en- 
ergy. Then  there  are  as  many  specific  energies  as 
there  are  end-organs,  and  a  like  number  of  rates  of 
vibration  auditively  distinguishable  by  us. 

Further,  we  not  only  distinguish  between  tones, 
but  we  assign  to  them  also  their  ordinal  places  in  a  se- 
ries. Of  three  tones  of  different  pitch,  we  recognise 
the  middle  one  immediately  as  such.  We  feel  imme- 
diately which  rates  of  vibration  lie  near  together  and 

IMach,  "Zur  Theorie  des  GehSrorgans"  {Sitzungsberickte  der  Wiener 
Akademie,  1863. 

2  Compare  my  "  Bemerkungen  zur  Lehre  vom  raumlichen  Sehen " 
{Fickte's  Zeitschrift  fUr  Philosophie,  1865). 

i Einleitung  in  die  Helmholtz' sche  Musikiheorie,  Graz,  1866.  See  the  Pref- 
ace and  pp.  23  et  seq.,  46  and  48.  ' 


128 


THE  ANALYSIS  OF  THE  SENSATIONS. 


which  lie  far  apart.  This  is  readily  enough  explained 
for  neighboring  tones.  For,  if  we  represent  the  vibra- 
tion-amplitudes of  a  certain  tone  symbolically  by  the 
curve  abc,  Fig.  35,  and  imagine  this  curve  gradually 
moved  in  the  direction  of  the  arrow,  then,  since  ne- 
cessarily several  organs  always  yield  simultaneous  re- 
sponses, neighboring  tones  will  always  have  faint, 
common  excitations.  But  distant  tones  also  possess  a 
certain  similarity ;  and  even  between  the  highest  and 
lowest  tones  we  can  detect  a  resemblance.  Conse- 
quently, in  accordance  with  the  principle  of  investiga- 
tion by  which  we  are  guided,  we  are  obliged  to  assume 

in  all  tone  -  sensations 
common  factors.  Conse- 
quently, again,  there  can- 
not be  as  many  specific 
^  energies  as  there  are  dis- 
tinguishable tones.  For 
the  understanding  of  the 
facts  with  which  we  are 
here  concerned,  it  suffices  to  assume  only  two  energies, 
which  are  excited  in  different  proportions  by  different 
rates  of  vibration.  Further  complexity  of  the  sensa- 
tions of  tone  is  not  excluded  by  these  facts,  but  on  the 
contrary  is  rendered  probable  by  phenomena  to  be  dis- 
cussed later. 

Careful  psychological  analysis  of  the  tonal  series 
leads  immediately  to  this  view.  But  even  supposing 
we  assume  a  special  energy  for  every  rod  of  Corti,  and 


Fig.  35. 


SENSATIONS  OF  TONE. 


129 


reflect  that  these  energies  are  similar  to  one  another, 
that  is,  contain  common  elements,  virtually  we  arrive 
at  the  same  conception.  For  let  us  assume,  merely 
in  order  to  have  a  definite  picture  before  us,  that,  in 
the  transition  from  the  lowest  to  the  highest  rates  of 
vibration,  the  tonal  sensation  varies  similarly  to  the 
color-sensation  in  passing  from  pure  red  to  pure  yel- 
low, say  by  the  gradual  admixture  of  yellow.  We  can 
fully  retain,  on  this  view,  the  idea  that  there  is  for 
every  distinguishable  rate  of  vibration  a  special  ap- 
propriate end-organ  ;  but  in  that  case  not  absolutely 
different  energies,  but  always  the  same  two  energies, 
only  in  different  proportions,  are  disengaged  by  the 
different  organs.^ 

9. 

How  does  it  happen,  now,  that  a  number  of  notes 
simultaneously  sounded  are  distinguished^  seeing  that 
we  should  naturally  expect  them  to  blend  into  a  single 
sensation ;  or  that  two  tones  of  different  pitch  do  not 
blend  to  a  mixed  tone  of  intermediate  pitch  ?  The 
fact  that  this  does  not  happen,  lends  a  still  more 
definite  shape  to  the  conception  which  we  have  to 
form.  The  case  is  probably  similar  to  that  of  a  grad- 
uated series  of  mixed  reds  and  yellows  situated  at  dif- 
ferent points  of  space,  which  are  likewise  distinguished 

IThe  view  that  different  end-organs  respond  to  different  rates  of  vibra- 
tion is  too  well  supported  by  the  production  of  beats  by  neighboring  tones, 
and  by  other  facts  adduced  by  Helmholtz,  and,  upon  the  whole,  too  valuable 
for  the  comprehension  of  the  phenomena,  to  be  again  relinquished.  The 
view  here  presented  utilises  the  facts  disclosed,  notably  by  Hering,  in  the 
analysis  of  color-sensations. 


I30  THE  ANALYSIS  OF  THE  SENSATIONS. 

and  do  not  blend.  As  a  fact,  the  sensation  which  ensues 
when  the  attention  passes  from  one  tone  to  another  is 
similar  to  that  which  accompanies  the  wandering  of 
the  fixation-point  in  the  field  of  vision.  The  tonal 
series  is  an  analogue  of  space,  but  of  a  space  of  one 
dimension  limited  in  both  directions  and  exhibiting 
no  symmetry  like  that,  for  instance,  of  a  straight  line 
running  from  right  to  left  in  a  direction  perpendicular 
to  the  median  plane.  It  more  resembles  a  vertical 
right  line,  or  one  running  from  the  front  to  the  rear 
in  the  median  plane.  But  while  colors  are  not  con- 
fined to  certain  points  in  space,  but  may  move  about, 
which  is  the  reason  we  so  easily  separate  space-sensa- 
tions from  color-sensations,  the  case  is  different  with 
tone-sensations.  A  particular  tone-sensation  can  oc- 
cur only  at  a  particular  point  of  the  said  one-dimen- 
sional space,  on  which  the  attention  must  in  each  case 
be  fixed  if  the  tone-sensation  in  question  is  to  be  dis- 
tinctly perceived.  We  may  now  imagine  that  differ- 
ent tone-sensations  have  their  origin  in  different  parts 
of  the  auditive  substance,  or  that,  in  addition  to  the 
two  energies  whose  ratio  determines  the  timbre  of 
high  and  deep  tones,  a  third  exists,  which  is  similar 
to  the  sensation  of  innervation,  and  which  comes  into 
play  in  the  fixation  of  tones.  Or  both  conditions  might 
occur  together.  At  present  it  may  be  regarded  as 
neither  possible  nor  necessary  to  come  to  a  conclusion 
in  the  matter. 

That  the  province  of  tone-sensation  offers  an  an- 


SENSATIONS  OF  TONE.  131 

alogy  to  space,  and  to  a  space  having  no  symmetry, 
unconsciously  expresses  itself  in  language.  We  speak 
of  high  tones  and  deep  tones,  not  of  right  tones  and 
left  tones,  although  our  musical  instruments  suggest 
the  latter  designation  as  a  very  natural  one. 

In  one  of  my  earliest  publications^  I  supported  the 
view  that  the  fixation  of  tones  was  connected  with  a 
varying  tension  of  the  tensor  tympani.  I  am  now  un- 
able to  maintain  this  view  in  the  light  of  subsequent 
observations  and  experiments  which  I  have  made. 
Nevertheless,  the  space-analogy  does  not  fall  to  the 
ground  for  this  reason;  but  merely  the  appropriate 
physiological  elevcvent  remains  to  be  discovered.  ^ 

IZur  Theorie  des  Gehdrorgans,  1863. 

2  The  supposition  that  the  processes  in  the  larynx  during  singing  have 
had  something  to  do  with  the  formation  of  the  tonal  series  I  likewise  noticed 
in  my  work  of  1863,  but  did  not  find  it  tenable.  Singing  is  connected  in  too 
extrinsic  and  accidental  a  manner  with  hearing  to  bear  out  such  an  hypothe- 
sis. I  can  hear  and  imagine  tones  far  beyond  the  range  of  my  own  voice.  In 
listening  to  an  orchestral  performance  with  all  the  parts,  or  in  having  an  hal- 
lucination of  such  a  performance,  it  is  impossible  for  me  to  think  that  my 
understanding  of  this  broad  and  complicated  sound-fabric  has  been  effected 
by  my  one  larynx,  which  is,  moreover,  no  very  practised  singer.  I  consider 
the  sensations  which,  in  listening  to  singing,  are  doubtless  occasionally  no- 
ticed in  the  larynx,  a  matter  of  subsidiary  importance,  like  the  pictures  of 
the  keys  touched  which,  when  I  was  more  in  practice,  sprang  up  immediately 
into  my  imagination  on  hearing  a  performance  on  the  piano  or  organ.  When 
I  imagine  music,  I  always  distinctly  hear  the  notes.  Music  can  no  more  come 
into  being  merely  through  the  motor  sensations  accompanying  musical  per- 
formances than  a  deaf  man  can  hear  by  watching  the  movements  of  players. 
I  cannot,  therefore,  agree  with  Strieker  on  this  point.  (Comp.  Strieker:  Du 
langage  et  de  la  musique.     Paris,  1885). 

Different  is  my  opinion  with  regard  to  Strieker's  views  on  language. 
(Comp.  Strieker,  Die  Sprachvorstelhmgen,  Vienna,  1880.)  It  is  true  that  in 
my  own  case  words  of  which  I  think  reverberate  loudly  in  my  ear.  More- 
over, I  have  no  doubt  that  thoughts  may  be  directly  excited  by  the  ringing  of 
a  housebell,  by  the  whistle  of  a  locomotive,  etc.,  and  that  small  children  and 
even  dogs  understand  words  which  they  cannot  repeat.  Nevertheless,  I  have 
been  convinced  by  Strieker  that  the  ordinary  and  most  familiar,  though  not 
the  only  possible  way  by  which  speech  is  comprehended,  is  really  motor,  and 


i 


132  THE  ANALYSIS  OF  THE  SENSATIONS, 

10. 

The  analogy  between  fixing  the  eyes  on  points  in 
space  and  fixing  the  attention  on  tones,  I  have  re- 
peatedly illustrated  by  experiments,  which  I  shall  cite 
again  here.  One  and  the  same  combination  of  two 
tones  sounds  different  according  as  we  fix  our  atten- 
tion upon  the  one  or  the  other.  Combinations  i  and 
2  in  the  annexed  cut  have  a  perceptibly  different  char- 

2  3  4  6  6 


d    I    i  bi    1=3 


ff=^ 


f  if 

acter  according  as  we  fix  our  attention  on  the  higher 
or  on  the  lower  note.  Persons  not  able  to  transfer 
their  attention  arbitrarily  will  be  helped  by  having 

that  we  should  be  badly  oflF  if  we  were  without  it.  I  can  cite  corroborations  of 
this  view  from  my  own  experience.  I  frequently  see  strangers  who  are  en- 
deavoring to  follow  my  remarks,  slightly  moving  their  lips.  If  a  person  tells 
me  his  place  of  residence  and  I  omit  to  repeat  the  street  and  number  of  the 
house  after  him,  I  am  certain  to  forget  the  address,  but  with  the  exercise  of 
this  precautionary  measure,  I  retain  it  perfectly  in  memory.  A  friend  told  me 
recently  that  he  had  stopped  reading  the  Indian  drama  Urvasi,  because  he 
had  great  diflftculty  in  spelling  out  the  names,  and  consequently  could  not 
retain  them  in  memory.  The  dream  of  the  deaf-mute,  which  Strieker  relates, 
is  intelligible  only  from  his  point  of  view.  In  fact,  on  calm  reflexion  this 
seemingly  paradoxical  relation  is  by  no  means  so  remarkable.  The  extent  to 
which  our  thoughts  move  in  accustomed  and  routine  channels  is  shown  by 
the  surprise  produced  by  witticisms.  Good  jokes  would  be  more  frequent  if 
our  minds  moved  less  in  ruts.  To  many  the  obvious  collateral  meanings  of 
words  never  suggest  themselves.  Who,  for  example,  in  using  the  names 
Smith,  Baker,  or  Taylor  thinks  of  the  occupations  designated !  To  adduce 
an  analogous  example  from  a  different  field,  I  may  state  (comp.  p.  51)  that  I 
immediately  recognise  writing  reflected  in  a  mirror  and  accompanying  its 
original,  as  symmetrically  congruent  with  the  latter,  although  I  am  not  able 
to  read  it  directly,  because  of  my  having  learned  writing  by  motor  methods, 
with  my  right  hand.  I  can  also  best  illustrate  by  this  example  why  I  do  not 
agree  with  Strieker  in  regard  to  music:  music  is  related  to  speech  as  orna- 
ment is  to  writing. 


SENSATIONS  OF  TONE. 


ZS3 


one  note  sound  later  than  the  other.  This  then 
draws  the  attention  after  it.  With  a  little  practice  it 
is  possible  to  decompose  a  chord  (as,  for  instance,  5) 
into  its  elements  and  to  hear  the  constituent  tones  by 
themselves  (as  in  6).  These  and  the  following  experi- 
ments are  better  and  more  convincingly  carried  out 
upon  a  physharmonica  than  on  a  piano,  owing  to  the 
greater  duration  of  the  tones. 

Especially  astonishing  is  the  phenomenon  pro- 
duced when  we  cause  one  note  of  a  cord,  on  which 
the  attention  is  fixed,  to  be  damped.  The  attention 
then  passes  over  to  the  note  nearest  to  it,  which  comes 
out  with  the  distinctness  of  a  note  that  has  just  been 
struck.  The  impression  made  by  the  experiment  is 
quite  similar  to  that  which  we  receive  when,  absorbed 
in  work,  we  suddenly  hear  the  regular  striking  of  the 
clock  emerge  into  distinctness  after  having  entirely 
vanished  from  consciousness.  In  the  latter  case  the 
entire  tonal  effect  passes  the  threshold  of  conscious- 
ness, whilst  in  the  former  a  part  is  augmented.  If  in 
7,  for  example,  we  fix  the  attention  upon  the  upper 


I 


£ 


5 


r — ^ ^-^:rrj_ 


^ 


note,  letting  go,  successively  from  above,  the  keys 
damping  the  other  notes,  the  effect  obtained  is  ap- 
proximately that  of  8.  If,  in  9,  we  fix  the  attention 
on  the  lowest  note,  and  proceed  in  the  reverse  order, 


134 


THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 


we  obtain  the  impression  represented  in  lo.  The 
same  chordal  combination  sounds  quite  different  ac- 
cording to  the  part  on  which  the  attention  is  fixed. 
If,  in  II  or  12,  I  fix  my  attention  on  the  upper  note. 


» 


i 


^ 


W 


'J2L 


r 


T 


^ 


s- 


the  timbre  alone  appears  to  be  altered.  But  if  in  ii, 
the  attention  be  fixed  upon  the  bass,  the  entire  acous- 
tic mass  will  seem  to  sink  in  depth;  while  in  12  it 
will  appear  to  rise  if  we  regard  closely  the  succession 
e-f.  It  is  quite  evident,  in  fine,  that  chords  act  the 
part  of  clangs  (or  compound  notes  embracing  both 
fundamentals  and  harmonics).  The  facts  here  ad 
vanced  remind  us  strongly  of  the  changing  impression 
received  when,  in  observing  an  ornamental  design,  the 
attention  is  alternately  fixed  on  different  points. 

We  may  also  recall  to  mind  here  the  involuntary 
wandering  of  the  attention  which  takes  place  during 
the  continuous  and  uniform  sounding  of  a  note  on  the 
harmonium,  where  if  the  note  lasts  several  minutes, 
all  the  overtones  will  of  themselves  successively  emerge 
into  full  distinctness.^  The  process  appears  to  point 
to  a  sort  of  fatigue  for  the  note  on  which  the  attention 
has  long  been  fixed.     This  fatigue,  moreover,  is  reu- 


I  Compare  my  EinUitung  in  die  Htlmholtz'scht  Mttsiktheorie,  p.  ag 


SENSATIONS  OF  TONE.  135 

dered  quite  probable  by  an  experiment  which  I  have 
described  at  length  in  another  place.  ^ 

The  relations  we  have  here  been  describing,  touch- 
ing sensations  of  tone,  might  be  illustrated  perhaps 
more  palpably  by  some  such  parallel  as  the  following. 
Suppose  that  our  two  eyes  were  capable  of  only  a  single 
movement,  that  they  could  only  follow,  by  changing 
motions  of  symmetrical  convergence,  the 
points  of  a  horizontal  straight  line  lying 
in  the  median  plane ;  and  suppose  that 
the  nearest  points  on  this  line  fixed  by 
the  eyes  were  pure  red,  and  those  farthest 
away,  corresponding  to  the  position  of 
parallelism,  were  pure  yellow,  while  be- 
tween them  lay  all  intermediate  shades  ; 

Fig.  36. 

then  the  system  of  sight-sensations  so 

constructed  would  quite  palpably  resemble  the  facts 

presented  by  sensations  of  tone. 

II. 

On  the  view  hitherto  developed,  an  important  fact, 
which  we  shall  now  state,  remains  unintelligible, 
though  its  explanation  is  absolutely  necessary  if  the 
theory  is  to  lay  any  claim  to  completeness.  If  two 
series  of  tones  be  begun  at  two  different  points  on  the 
scale,  but  be  made  to  maintain  throughout  the  same 
ratios  of  vibration,  we  shall  recognise  in  both  the  same 


1  Compare  my  Grundlinien  der  Lehre  von  den  Bewegungsempfindungen, 
p.  58. 


136  THE  ANALYSIS  OF  THE  SENSATION'S. 

melody,  by  a  mere  act  of  sensation,  just  as  readily  and 
immediately  as  we  recognise  in  two  geometrically  sim- 
ilar figures,  similarly  situated,  the  same  form.  Like 
melodies,  differently  situated  on  the  scale,  might  be 
denominated  tonal  constructs  of  like  tonal  fornix  or  they 
might  be  denominated  similar  tonal  constructs,  from 
their  space-analogues. 

Even  in  a  series  of  only  two  tones,  the  sameness 
of  the  vibrational  ratios  is  at  once  recognised.  Thus 
the  series  c-f,  d-g,  e-a,  etc.,  which  have  all  the  same 
vibrational  ratios  (3:4),  are  immediately  recognised  as 
like  intervals,  2lS  fourths.  Such  is  the  fact,  in  its  sim- 
plest form.  The  ability  to  pick  out  and  recognise  in- 
tervals is  the  first  thing  required  of  the  student  of 
music  who  is  desirous  of  becoming  thoroughly  familiar 
with  his  province. 

In  a  little  work,^  well  worth  reading,  by  Mr.  E. 
Kulke,  mention  is  made,  bearing  on  this  point,  of  an 
original  method  of  instruction  by  P.  Cornelius — a  de- 
scription of  which  I  will  here  complete  from  Kulke's 
own  lips.  According  to  Cornelius,  it  is  a  wonderful 
help  in  the  recognition  of  intervals  to  make  note  of 
particular  pieces  of  music,  folk-songs,  etc.,  which  be- 
gin with  these  intervals.  The  Overture  to  Tannhauser, 
for  example,  begins  with  a  fourth.  If  I  hear  a  fourth 
I  at  once  remark  that  the  series  of  tones  is  the  same 
as  that  beginning  the  Overture  to  Tannhauser  and 


IE.    Kulke,    Ueber  die   Umbildung  drr  Mtlodie.    Ein  Beitrag  %ur  Ent- 
micklungsUhre.    Prague.    Calve.     1884. 


SENSATIONS  OF  TONE.  X37 

by  this  means  recognise  the  interval.  In  like  manner, 
the  Overture  to  Fidelio  may  be  used  as  the  represen- 
tative of  the  third  ;  and  so  on.  This  excellent  device, 
which  I  have  put  to  the  test  in  my  lectures  on  acous- 
tics and  have  found  very  effective,  apparently  compli- 
cates matters.  One  would  naturally  suppose  that  it 
would  be  easier  to  make  note  of  an  interval  than  of  a 
melody.  Nevertheless,  a  melody  offers  a  greater  hold 
to  memory  than  does  an  interval,  just  as  an  individual 
countenance  is  more  easily  remarked  and  associated 
with  a  name  than  is  a  certain  facial  angle  or  a  nose. 
Every  one  makes  note  of  faces  and  associates  with 
them  names  ;  but  Leonardo  da  Vinci  arranged  noses 
in  a  system. 

And  as  every  interval  in  a  series  of  tones  is  made 
perceptible  in  characteristic  manner,  so  it  is  with  the 
harmonic  combinations  of  tones.  Every  third,  every 
fourth,  every  major  or  minor  triad  has  its  character- 
istic color,  by  which  it  is  recognised  independently  of 
the  pitch  of  the  fundamental,  and  independently  of 
the  number  of  beats,  which  rapidly  increase  with  in- 
creasing pitch. 

A  tuning-fork  held  before  one  ear  is  very  feebly 
heard  by  the  other  ear.  If  two  slightly  discordant,  beat- 
ing tuning-forks  are  held  in  front  of  the  same  ear,  the 
beats  are  very  distinct.  But  if  one  of  the  forks  be 
placed  before  one  ear,  and  the  other  before  the  other, 
the  beats  will  be  greatly  weakened.  Two  forks  of  har- 
monic interval  always  sound  slightly  rougher  before 


138  THE  ANALYSIS  OF  THE  SENSATIONS. 

one  ear.  But  the  character  of  the  harmony  is  pre- 
served when  one  is  placed  before  each  ear.^  Discord 
also  remains  quite  perceptible  in  this  experiment. 
Harmony  and  discord  are  certainly  not  determined  by 
beats  alone. 

In  melodic  as  well  as  in  harmonic  combinations, 
notes  whose  rates  of  vibrations  bear  to  one  another 
some  simple  ratio,  are  distinguished  (i)  by  their  agree- 
ablenesSy  and  (2),  by  a  sensation  characteristic  of  this 
ratio.  As  for  the  agreeable  quality,  there  is  no  deny- 
ing but  this  is  partly  explained  by  the  coincidence  of 
the  overtones,  and,  in  the  case  of  harmonic  combi- 
nation, by  the  consequent  effacement  of  the  beat?,  re- 
sulting always  where  the  ratios  of  the  numbers  repre- 
senting the  vibrations  satisfy  certain  simple  conditions. 
But  the  experienced  and  unprejudiced  student  of  mu- 
sic is  not  entirely  satisfied  with  this  explanation.  He 
is  disturbed  by  the  preponderant  role  accorded  to  the 
accident  of  acoustic  color,  and  notices  that  tones  fur- 
ther stand  to  each  other  in  a  positive  relation  of  con- 
trastj  like  colors,  except  that,  in  the  case  of  colors,  no 
such  definite  agreeable  relations  can  be  specified. 

The  fact  that  a  sort  of  contrast  really  does  exist 
among  tones  is  almost  forced  upon  our  notice.  A 
smooth,  unchanging  tone  is  something  very  unpleas- 
ing  and  characterless,  like  a  single  uniform  color  en- 
veloping our  entire  surroundings.     A  lively  effect  is 


1  Compare  Fechner,    Ueber  einigt   Vtrhaltnisse  des  binocularen  Sevens, 
Leipsic,  i860,  p.  536. 


SENSATIONS  OF  TONE.  139 

produced  only  on  the  addition  of  a  second  tone,  a  sec- 
ond color.  In  like  manner,  if  we  cause  a  tone  gradu- 
ally to  mount  in  pitch,  as  in  experiments  with  the 
siren,  all  contrast  is  lost.  Contrast  exists,  however, 
between  tones  farther  apart,  and  not  merely  between 
those  immediately  following  one  another,  as  the  ac- 
companying example  will  show.     Passage  2  sounds 

12  3  4  5 


w 


^^tjli-^ 


quite  different  after  i  from  what  it  does  alone,  3  sounds 
different  from  2,  and  even  5  different  from  4  imme- 
diately following  3. 

12. 

Let  us  turn  now  to  the  second  point,  the  charac- 
teristic sensation  corresponding  to  each  interval,  and 
ask  if  this  can  be  explained  on  the  current  theory.  If 
a  fundamental  n  be  melodically  or  harmonically  com- 
bined with  its  third  m,  the  fifth  harmonic  of  \\\&  first 
note  {^n)  will  coincide  with  the  fourth  of  the  second 
note  (4^).  This,  according  to  the  theory  of  Helm- 
holtz,  is  the  common  feature  characterising  all  third- 
combinations.  If  I  combine  the  notes  C  and  E,  or  F 
and  A,  representing  their  harmonics  in  the  cut  on  the 
next  page,  then,  as  a  fact,  in  the  one  case  the  harmonics 
marked  I  and  in  the  other  those  marked  T  coincide  ; 
and  in  both  cases  the  coincidence  is  between  the  fifth 
harmonic  of  the  lower  and  the  fourth  harmonic  of  the 


I40  THE  ANALYSIS  OF  THE  SENSATIONS. 

higher  note.  Be  it  noted,  however,  that  this  com- 
mon feature  exists  solely  for  the  understanding,  being 
the  result  of  a  purely  physical  and  intellectual  anal- 
ysis, and  has  nothing  to  do  with  sensation.  For  sensa- 
tion the  real  coincidence  in  the  first  case  is  between 
the  e's,  and  in  the  second  between  the  a's,  which  are 
entirely  different  notes.    On  the  assumption  that  there 


c 

g 

C 

e 

g 

b-flat 

c 

2» 

3« 

4« 

5« 

tn 

7» 

8» 

^^ 

e 

b 

e 

g 

-sharp 

b 

d 

e 

ZtH 

3*» 

4*» 

yn 

6m 

jm 

8m 

t 


F 

i 

c 

1 

a 

c 

e-flat 

f 

n 

2n 

3« 

4« 

5» 

6« 

7« 

8*. 

t 

A 

a 

e 

a 

c-sharp 

e 

i 

a 

m 

2M 

3fft 

4/« 

5'« 

6m 

7M 

8m 

exists  for  every  distinguishable  rate  of  vibration  an 
appurtenant  specific  energy,  we  are  obliged,  more 
than  on  any  other  theory,  to  ask  where  is  the  common 
component  of  sensation  hidden  that  characterises  every 
third  combination? 

I  must  insist  on  this  distinction  of  mine  not  being 
regarded  as  a  piece  of  pedantic  hair-splitting.  I  pro- 
pounded the  question  involving  it  about  twenty  years 
ago,  at  the  same  time  with  my  question  as  to  wherein 


SENSATIONS  OF  TONE. 


141 


physiological  similarity  of  form,  as  distinguished  from 
geometrical,  consisted  ;  and  it  is  not  a  whit  more  un- 
necessary than  was  that,  whose  superfluity,  too,  in  the 
issue,  was  disproved.  If  we  are  to  suffer  a  physical 
or  mathematical  characteristic  of  the  third  interval  to 
stand  as  a  mark  of  the  Xh^xdi-sensation,  then  we  should 
content  ourselves,  as  Euler  did,^  with  the  coincidence 
of  every  fourth  and  fifth  vibration — a  conception  which 
was,  after  all,  not  so  bad,  provided  it  could  be  supposed 
that  sound  continued  its  course  in  the  nerve- tracts, 
also,  as  periodic  motion,  a  view  which  even  A.  Seebeck 
(JPogg.  Ann.  J  Vol.  68)  regarded  as  possible.  With  re- 
gard to  this  particular  point,  Helmholtz's  coincidence 
of  5«  and  /^m  is  in  no  respect  less  symbolical  and  does 
not  offer  greater  enlightenment. 

13. 

So  far  I  have  presented  my  arguments  with  the 
conviction  that  I  should  not  find  it  necessary  to  make 
a  single  retrograde  step  of  importance.  This  feeling 
does  not  accompany  me  in  the  same  measure  in  the 
development  of  the  following  hypothesis,  which,  in 
all  its  essential  features,  was  suggested  to  me  a  long 
time  ago.  Yet  the  hypothesis  may  at  least  serve  to 
clear  up  and  illustrate,  from  the  positive  side  also,  the 
requirement  which  I  believe  a  more  complete  theory 
of  tone-sensations  is  bound  to  meet. 

We  will  begin  by  supposing  that  it  is  an  extremely 

lEulcr,  Ttniamtn  novat  tht»riat  musicae,  Petropoli,  1789,  y.  36. 


142 


THE  ANALYSIS  OF  THE  SENSATIONS. 


important  vital  condition  for  an  animal  of  simple  or- 
ganisation to  perceive  slight  periodic  motions  of  the 
medium  in  which  it  lives.  If  (owing  to  the  relatively 
excessive  size  of  its  organs,  and  its  consequent  lack 
of  receptivity  for  such  rapid  changes)  its  attention  is 
too  sluggishly  transferred,  the  period  of  the  impinging 
vibrations  is  too  short,  or  their  amplitude  too  small, 
to  permit  the  single  phases  of  the  excitation  to  enter 
consciousness,  it  may  nevertheless  be  possible  under 
certain  conditions  for  the  animal  to  perceive  the  ac- 
cumulated sensation-effects  of  the  oscillatory  excita- 
tion. The  organ  of  hearing  will  outstrip  the  organ  of 
touch.  ^  Now  an  end-organ  capable  of  vibration  (say 
an  auditory  cilium)  responds,  by  virtue  of  its  physical 
qualities,  not  to  every  rate  of  vibration,  nor  to  one  only, 
but  ordinarily  to  several^  at  a  considerable  distance 
apart.*  Therefore,  as  soon  as  the  whole  continuum 
of  vibrational  rates  between  certain  limits  becomes  of 
importance  for  the  animal,  a  small  number  of  end- 
organs  no  longer  suffice,  but  the  need  of  a  whole  series 
of  such  organs  of  graduated  sonancy  arises.  The  or- 
gan of  Corti  is  regarded  as  such  a  system. 

It  can  hardly  be  expected,  however,  that  a  mem- 
ber of  Corti's  organ  will  respond  to  only  one  rate  of 

lit  is  questionable  therefore  whether  animals  which  have  so  small  a 
measure  of  time  that  their  voluntary  movements  produce  a  musical  note  hear 
in  the  ordinary  sense,  or  whether  with  them  that  is  not  rather  touch  which 
makes  on  us  the  impression  of  hearing.  Compare,  for  example,  the  admir- 
able experiments  and  observations  of  V.  Graber  ("  Die  Chordotonalen  Or- 
i(ane,"  Arrh./Ur  Microskop,  Anat.,  XX.,  p.  506;. — Compare  also  my  Bewtgung** 
tmpfindung€n ,  p.  123. 

SAb  V.  Hensen,  for  example,  has  observed. 


SENSATIONS  OF  TONE. 


M3 


vibration.  On  the  contrary,  we  must  suppose  that  it 
responds  with  enfeebled  but  graduated  intensity  (per- 
haps from  being  divided  by  nodes)  to  the  rates  of 
vibration  in,  yt,  \n,  etc.,  as  also  to  the  rates  of  vi- 
bration «/2,  «/3,  ^2/4,  etc.  Inasmuch  as  the  assump- 
tion of  a  special  energy  for  each  rate  of  vibration  has 
proved  untenable,  we  may  imagine,  agreeably  to  re- 
marks made  above,  that  in  the  first  place,  only  two 
sensation-energies.  Dull  (Z>)  and  Clear  (C),  are  ex- 
cited. The  resultant  sensation  we  will  represent  sym- 
bolically (somewhat  as  we  do  in  mixed  colors)  by 
pD-\-qC\  or,  making /-|-^  =  1  and  regarding  ^  as  a 
function /(;2)  of  the  rate  of  vibration,^  by  [1 — f{p)\ 
D  -\-f{n)  C.  The  sensation  arising  will  now  correspond 
to  the  number  of  the  vibrations  producing  the  oscillatory 
excitation,  on  whatever  member  of  Corti's  series  the 
excitation  may  light.  And  consequently  the  current 
conception  will  not  be  materially  disturbed  by  the  new 
hypothesis.  For,  since  the  member  Rn  responds  most 
powerfully  to  n,  and  only  in  a  much  more  enfeebled 
degree  to  in,  3^,  or  to  nji,  n/^,  E„  vibrating  with  n 
even  in  case  of  an  aperiodic  impulse,  therefore  the 
sensation  [1  — f(n)\  D  -\-f{n)  C  will  still  be  predom- 
inantly associated  with  Rn- 

Well-attested  cases  of  double  hearing  (compare 
Stumpf,  loc.  cit.y  p.  206,  et  seq.)  point  forcibly  to  the 
conclusion  that  the  ratios  in  which  the  energies  D  and 
C  are  disengaged  are  dependent  upon  the  end-organ, 

IThus,  to  take  a  very  simple  example,  we  might  make/"(«)  =  k  .  log». 


144  THE  ANALYSIS  OF  THE  SEN  ATIONS. 

and  not  upon  the  rate  of  vibration — a  conclusion  which 
would  also  not  affect  our  conception. 

A  member  R„y  accordingly,  responds  powerfully  to 
«,  and  also,  though  more  weakly,  to  2«,  3«,  .  .  .  .  , 
«/2,  «/3  ....  with  the  sensations  belonging  to  these 
rates  of  vibration.  It  is,  however,  extremely  improb- 
able that  exactly  the  same  sensation  is  excited  whether 
Rn  responds  to  «,  or  whether  Rn  responds  to  n.  On 
the  contrary,  it  is  probable  that  every  time  the  mem- 
bers of  Corti's  series  respond  to  a  partial  tonCy  the  sen- 
sation receives  a  weak  supplementary  colorings  which  we 
will  represent  symbolically,  for  the  fundamental  tone 
by  Zj,  for  the  overtones  by  Z^,  Zg,  .  .  .  .,  and  for  the 
undertones  by  Zi,  Zi,.  .  .  .  On  this  supposition,  sen- 
sations of  tone  would  be  somewhat  richer  in  composi- 
tion than  would  follow  from  the  formula  [1  — /(«)]  D 
+/(»)  C'  The  sensations  which  Corti's  series,  as  ex- 
cited by  the  fundamentals,  yields,  constitute  a  province 
with  the  supplementary  coloring  Z^,  the  excitation  of 
the  same  series  by  the  first  overtone  yields  a  special 
province  of  sensation  with  the  supplementary  coloring 
Z,,  etc.  The  Z's  may  be  either  unchanging  elements, 
or  may  themselves,  again,  consist  of  two  components, 
i/'and  Vy  and  form  series  representable  by  [1 — /(«)] 
U-\-  f{n)  V.  But  at  present  the  decision  on  this  last 
point  is  immaterial. 

It  is  true  that  Xh.Q. physiological  ^^vci.^Ti\.s  Z^,  Z^, .  .  .  . 
have  yet  to  be  found.  Yet  the  very  perception  that 
they  have  to  be  sought  seems  to  me  of  importance. 


SENSATIONS  OF  TONE. 


145 


Let  us  see  what  form  the  province  of  tone-sensations 
would  take  on  if  we  regarded  Z^,  Z^,  .  .  .  .  as  given. 
Our  example  is  a  melodic  or  harmonic  major- 
third  combination,  whose  rates  of  vibration  are  n^\p 
and  m  =  ^p',  the  lowest  of  the  overtones  common  to 
the  two  is  5/2  =  4^  =  20/,  the  highest  of  the  under- 
tones common  to  the  two  is  /.  Then  we  obtain  the 
following  table  i^ 


The    members    of 
the  Corti  series : 


Rp 


Ra^ 


^S> 


J?ao/ 


§t3  a 


respond  to  the  rates 
of  vibration : 


4A  5/ 


4/ 


with    the    supple- 
mentary sensa- 
tions: 


^4.^5 


5> 


Zx 


4/  = 


5/  = 


5 
20/ 


^f^i 


> 

a 
o  o 


they  also  respond 
to  the  rates  of  vi- 
bration : 


20/  =  5  (4/) 


20/ =  4  (5/) 


with   the    supple- 
mentary sensa- 
tions : 


Thus  in  the  third  combination,  the  supplementary 
sensations  Z^,  Z^,  and  Zi,  Z,,  which  are  characteristic 
of  the  third,  make  their  appearance  even  when  the 


1  It  will  be  observed  that  the  analysis  of  the  tone-sensations  here  offered 
follows  the  same  path  as  the  current  analysis  of  color-sensations.  In  both 
cases,  inquirers  started  with  the  view  that  to  the  endless  physical  differences 
presented  in  the  world  there  corresponded  endless  physiological  differences. 
Conformably  to  the  principle  of  parallelism,  the  number  of  the  sensation- 
elements  has  in  both  cases  been  reduced. 


146  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

notes  contain  no  overtones,  while  the  former  (Z^,  Z^) 
are  strengthened  when,  either  in  the  open  air  or  at 
least  in  the  ear,  overtones  do  occur.  The  diagram 
may  be  easily  generalised  to  include  any  interval. 

These  supplementary  colorings,  though  scarcely 
noticeable  in  single  tones,  or  in  running  continuously 
through  the  scale,  become  conspicuous  in  combina- 
tions of  tones  having  certain  rates  of  vibrations,  just 
as  the  contrasts  of  faintly  colored,  almost  white  lights 
become  vivid  when  these  are  brought  together.  And, 
furthermore,  the  same  contrast-colorings  always  corre- 
spond to  the  same  ratios  of  vibrations,  no  matter  what 
the  pitch. 

In  this  manner  it  is  intelligible  how  tones  may 
receive,  by  melodic  and  harmonic  combination  with 
others^  the  most  varied  colorings,  which  are  wanting 
to  them  when  singly  sounded. 

The  elements  Z^,  Z,  .  .  .  must  not  be  conceived  as 
unvarying  and  fixed  in  number.  On  the  contrary,  it 
is  to  be  supposed  that  the  number  of  perceptible  Z's 
depends  on  the  organisation,  on  the  training  of  the 
ear,  and  on  the  attention.  According  to  this  concep- 
tion, the  ear  does  not  directly  cognise  ratios  of  vibra- 
tions but  only  the  supplementary  colorings  conditioned 
by  these.  The  tonal  series  symbolically  represented 
by  [I — /(«)]^  +  /(«)  ^  is  not  infinite  but  limited. 
Since  /(«)  may  vary  between  the  values  0  and  1,  D 
and  C  are  the  extremes,  the  terminal  sensations  cor- 
responding to  the  lowest  and  highest  tones.     If  the 


SENSATIONS  OF  TONE.  147 

number  of  vibrations  sinks  considerably  below  or  rises 
considerably  above  that  of  the  fundamental  of  the 
longest  and  the  shortest  Corti  fibre,  a  weak  response 
only  will  take  place,  but  no  alteration  of  the  quality 
of  the  sensation.  Likewise,  the  sensation  due  to  the 
interval  must  disappear  in  the  neighborhood  of  the 
limits  of  hearing ;  first,  because  in  general  differences 
between  sensations  of  tone  cease  at  this  point,  and, 
further,  because  at  the  upper  boundary  the  members 
of  the  Corti  series  susceptible  of  being  excited  by  the 
undertones,  are  lacking,  as  are  also  at  the  lower  boun- 
dary those  which  react  on  the  overtones. 


14. 

Passing  in  review  again  the  conception  gained,  we 
see  that  with  few  exceptions  the  conclusions  reached 
by  Helmholtz  may  be  all  retained.  Noises  and  com- 
posite sounds  may  be  decomposed  into  musical  tones. 
For  every  perceptible  rate  of  vibration  there  corres- 
ponds a  particular  nervous  end-organ.  In  place  of 
the  numerous  specific  energies  required  by  this  theory, 
however,  we  substitute  but  two^  which  render  the  re- 
lationship of  all  tonal  sensations  intelligible,  and  by 
the  r61e  which  we  assign  to  the  attention,  likewise 
enable  us  to  keep  perceptually  distinct,  several  tones 
when  sounded  together.  By  the  hypothesis  of  the 
multiple  response  of  the  members  of  the  Corti  series, 
and  that  of  supplementary  acoustic  colorings,  the  sig- 


148  THE  ANALYSIS  OF  THE  SENSATIONS. 

nificance  of  accidental  acoustic  tints  is  diminished, 
and  we  get  a  glimpse  of  the  direction  in  which,  not- 
ably on  the  ground  of  musical  facts,  the  positive  char- 
acteristics of  intervals  are  to  be  sought.  Finally,  by 
the  latter  conception.  Von  Oettingen's  principle  of 
duality  acquires  a  basis,  which  might  perhaps  com- 
mend itself  to  this  investigator  himself  better  than  his 
assumption  of  ** memory";  while  at  the  same  time  it 
becomes  manifest  why  the  duality  cannot  be  a  perfect 
symmetry. 

15- 

To  a  person  accustomed  to  looking  at  things  from 
the  point  of  view  of  the  theory  of  evolution,  the  high 
development  of  modern  music  as  well  as  the  spon- 
taneous and  sudden  appearance  of  great  musical  talent 
seem,  at  first  glance,  a  most  singular  and  problematic 
phenomenon.  What  could  this  remarkable  develop- 
ment of  the  power  of  hearing  have  had  to  do  with  the 
preservation  of  the  species?  Does  it  not  far  exceed 
the  measure  of  the  necessary  or  the  useful?  What  can 
possibly  be  the  significance  of  a  fine  discriminative 
sense  of  pitch?  Of  what  use  to  us  is  a  perceptive 
sense  of  intervals,  or  of  the  acoustic  colorings  of  or- 
chestral music? 

As  a  matter  of  fact,  the  same  question  may  be  pro- 
posed with  reference  to  every  art,  no  matter  from  what 
province  of  sense  its  material  is  derived.  The  ques- 
tion is  pertinent,  also,  with  regard  to  the  intelligence 


SENSATIONS  OF  TONE,  149 

of  a  Newton,  an  Euler,  or  their  like,  which  apparently 
far  transcends  the  necessary  measure.  But  the  ques- 
tion is  most  obvious  with  reference  to  music,  which 
satisfies  no  practical  need  and  for  the  most  part  de- 
picts nothing.  Music,  however,  is  closely  allied  to 
the  decorative  arts.  In  order  to  be  able  to  see,  a  per- 
son must  have  the  power  of  distinguishing  the  direc- 
tions of  lines.  Having  difine  power  of  distinction,  such 
a  person  may  acquire,  as  a  sort  of  collateral  product 
of  his  education,  a  feeling  for  agreeable  combinations 
of  lines.  The  case  is  the  same  with  the  sense  of  color- 
harmony  following  upon  the  development  of  the  power 
of  distinguishing  colors,  and  so,  too,  it  undoubtedly 
is  with  respect  to  music. 

We  must  bear  in  mind  that  talent  and  genius, 
however  gigantic  their  achievements  may  appear  to  us, 
constitute  but  a  slight  departure  from  normal  endow- 
ment. Talent  may  be  resolved  into  the  possession  of 
psychical  power  slightly  above  the  average  in  a  certain 
province.  And  as  for  genius,  it  is  talent  supplemented 
by  a  capacity  of  adaptation  extending  beyond  the 
youthful  period,  and  by  the  retention  of  freedom  to 
overstep  routine  barriers.  The  naivete  of  the  child 
delights  us,  and  produces  almost  always  the  impres- 
sion of  genius.  But  this  impression  as  a  rule  quickly 
disappears,  and  we  perceive  that  the  very  same  utter- 
ances which,  as  adults,  we  are  wont  to  ascribe  to  free- 
dom, have  their  source,  in  the  child,  in  a  lack  of  fixed 
character. 


I50  THE  ANALYSIS  OF  THE  SENSATIONS. 

Talent  and  genius,  as  Weismann  has  aptly  shown,* 
do  not  make  their  appearance  slowly  and  by  degrees 
in  the  course  of  generations  ;  nor  can  they  be  the  re- 
sult of  accumulated  effort  and  practice  on  the  part 
of  ancestors  ;  but  they  manifest  themselves  spontan- 
eously and  suddenly.  Taken  in  connexion  with  the 
preceding,  this,  too,  is  intelligible,  if  we  will  but  re- 
flect that  descendants  are  not  exact  reproductions  of 
their  ancestors,  but  exhibit  the  qualities  of  the  latter 
with  some  variations,  now  slightly  diminished,  now 
slightly  augmented  in  amount. 

1  Weismann,  Ueber  die  Vererbung,  Jena,  1883,  (English  translation,  Claren< 
don  Press,  Oxford,  1889,)  p.  43. 


PHYSICS. 


INFLUENCE    OF   THE    PRECEDING    INVESTIGATIONS 
ON  THE  MODE  OF  ITS  CONCEPTION.^ 


WHAT  gain  does  physics  derive  from  the  preced- 
ing investigations  ?  In  the  first  place,  a  very 
wide-spread  prejudice  is  removed,  and  with  it,  a  bar- 
rier. There  is  no  rift  between  the  psychical  and  the 
physical,  no  within  and  without^  no  sensation  to  which 
an  outward,  different  thing  corresponds.  There  is  but 
one  kind  of  elements^  out  of  which  this  supposititious 
within  and  without  is  formed — elements  which  are 
themselves  within  and  without  according  to  the  light 
in  which,  for  the  time  being,  they  are  viewed. 

2. 

The  world  of  sense  belongs  to  the  physical  and 
the  psychical  domain  alike.     As,  in  studying  the  be- 

1 1  have  partly  discussed  the  questions  considered  in  this  chapter,  before. 
(See  my  Erhaltung  der  Arbeit,  Prague,  Calve,  1872,  and  also  the  essay  on 
"The  Economical  Nature  of  Physicial  Inquiry,"  first  published  in  1882,  and 
now  in  my  Popular  Scientific  Lectures,  Chicago,  1894.)  With  regard  to  the  idea 
of  concepts  as  labor-saving  instruments,  Prof.  W.  James,  of  Harvard  Uni- 
versity, has,  in  conversation,  directed  my  attention  to  points  of  agreement 
between  my  writings  and  his  essay  on  "The  Sentiment  of  Rationality" 
{Mind,  Vol.  IV.,  p.  317,  July,  1879).  This  essay,  written  with  refreshing  vigor 
and  impartiality,  will  be  perused  by  every  one  with  pleasure  and  profit. 


152  THE  ANALYSIS  OF  THE  SENSATIONS. 

havior  of  gases,  by  disregarding  variations  of  tempera- 
ture we  reach  Mariotte's  law,  but  by  expressly  con- 
sidering them,  Gay  Lussac's,  while  throughout  our 
object  of  investigation  remains  the  same,  so,  too,  we 
study  physics  in  its  broadest  signification  when  in 
searching  into  the  connexions  of  the  world  of  sense 
we  leave  the  body  entirely  out  of  account,  whereas  we 
pursue  the  psychology  of  the  senses  when  we  direct  our 
main  attention  to  the  body  and  above  all  to  our  ner- 
vous system.  Our  body,  like  every  other,  is  part  of 
the  world  of  sense  ;  the  boundary-line  between  the 
physical  and  the  psychical  is  solely  practical  and  con- 
ventional. If,  for  the  higher  purposes  of  science,  we 
erase  this  dividing-line,  and  consider  all  connexions 
as  equivalent,  new  paths  of  investigation  cannot  fail  to 
be  opened  up. 

3. 
We  must  regard  it  as  an  additional  gain  that  the 
physicist  is  now  no  longer  overawed  by  the  traditional 
intellectual  implements  of  physics.  If  ordinary  '<  mat- 
ter" must  be  regarded  merely  as  a  highly  natural, 
unconsciously  constructed  mental  symbol  for  a  com- 
plex of  sensuous  elements,  much  more  must  this  be 
the  case  with  the  artificial  hypothetical  atoms  and 
molecules  of  physics  and  chemistry.  The  value  of 
these  implements  for  their  special,  limited  purposes 
is  not  one  whit  destroyed.  As  before,  they  remain 
still  economical  symbolisations  of  the  world  of  experi- 
ence. But  we  have  as  little  right  to  expect  from  them, 


PHYSICS.  ,53 

as  from  the  symbols  of  algebra  (to  use  an  apposite 
analogue),  more  than  we  have  put  into  them,  and  cer- 
tainly not  more  enlightenment  and  revelation  than 
from  experience  itself.  We  are  on  our  guard  now, 
even  in  the  province  of  physics,  against  overestimat- 
ing the  value  of  our  symbols.  Still  less,  therefore, 
should  the  monstrous  idea  ever  enter  our  heads  of  em- 
ploying atoms  to  explain  psychical  processes ;  seeing 
that  atoms  are  but  the  symbols  of  certain  peculiar 
complexes  of  sensuous  elements  which  we  meet  with 
in  the  narrow  domain  of  physics. 

4- 
The  sciences  may  be  distinguished  according  to 
the  matter  of  which  they  treat,  as  also  by  their  man- 
ner of  treating  it.  Further,  all  science  has  for  its  aim 
the  representation  of  facts  in  thought,  either  iox  practical 
ends,  or  for  removing  intellectual  discomfort.  Resum- 
ing the  terminology  of  the  ''Introductory  Remarks," 
science,  it  may  be  said,  arises  where  in  any  manner 
the  elements  ABC  ...  or  the  elements  KLM .  .  .  are 
reproduced  or  representatively  mimicked  by  the  ele- 
ments a^y.  .  .  .  ,  or  the  latter  by  one  another.  For 
example,  physics  (in  its  broadest  signification)  arises 
through  representatively  reproducing  by  apy .  .  .  the 
elements  ABC  in  their  relations  to  one  another ;  the 
physiology  or  psychology  of  the  senses,  through  repro- 
ducing in  like  manner  the  relations  oi  A  B  C  .  .  .  to 
KLM .  .  .  ;  physiology,  through  reproducing  the  rela- 


154  TH^  ANALYSIS  OF  THE  SENSATIONS. 

tions  of  KLM ,  .  .  to  one  another  and  to  ABC .  .  .  ; 
while  the  reproducing  of  the  afiy .  .  .  themselves  by 
other  aPy  leads  to  the  psychological  sciences  proper. 
Now  one  might  be  of  the  opinion,  say,  with  respect 
to  physics,  that  the  portrayal  of  the  sense-given  facts 
is  of  less  importance  than  the  atoms,  forces,  and  laws 
by  which  they  are  portrayed,  and  which  form,  so  to 
speak,  the  nucleus  of  the  sense-given  facts.  But  un- 
biassed reflexion  discloses  that  every  practical  and  in- 
tellectual need  is  satisfied  the  moment  our  thoughts 
have  acquired  the  power  to  represent  the  facts  of  the 
senses  completely.  Such  representation,  consequently, 
is  the  end  and  aim  of  physics ;  while  atoms,  forces, 
and  laws  are  merely  means  facilitating  the  representa- 
tion. Their  value  extends  as  far,  and  as  far  only,  as 
the  help  they  afford. 

5. 

Our  knowledge  of  a  natural  phenomenon,  say  of 
an  earthquake,  is  as  complete  as  possible  when  our 
thoughts  so  marshal  before  the  eye  of  the  mind  all  the 
relevant  sense-given  facts  of  the  case  that  they  may 
be  regarded  almost  as  a  substitute  for  the  latter,  and 
the  facts  appear  to  us  as  old  familiar  figures,  having 
no  power  to  occasion  surprise.  When,  in  imagina- 
tion, we  hear  the  subterranean  thunders,  feel  the  oscil- 
lation of  the  earth,  figure  to  ourselves  the  sensation 
produced  by  the  rising  and  sinking  of  the  ground,  the 
cracking  of  the  walls,  the  falling  of  the  plaster,  the 


PHYSICS. 


155 


movement  of  the  furniture  and  the  pictures,  the  stop- 
ping of  the  clocks,  the  rattling  and  smashing  of  win- 
dows, the  wrenching  of  the  door-posts,  the  jamming 
of  the  doors ;  when  we  see  in  mind  the  oncoming  un- 
dulation passing  over  a  forest  as  lightly  as  a  gust  of 
wind  over  a  field  of  grain,  breaking  the  branches  of 
the  trees  ;  when  we  see  the  town  enveloped  in  a  cloud 
of  dust,  hear  the  bells  begin  to  ring  in  the  towers ; 
further,  when  the  subterranean  processes,  which  are 
at  present  unknown  to  us,  shall  stand  out  in  full  sen- 
suous reality  before  our  eyes,  so  that  we  shall  see  the 
earthquake  advancing  as  we  see  a  waggon  approaching 
in  the  distance  till  finally  we  feel  the  earth  shaking  be- 
neath our  feet, — then  more  insight  than  this  we  cannot 
have,  and  more  we  do  not  require.  If  we  cannot  com- 
bine the  partial  facts  in  their  right  and  required  pro- 
portions without  the  aid  of  certain  auxiliary  concep- 
tions drawn  from  mathematics,  it  yet  remains  true  that 
the  latter  merely  enable  our  thoughts  to  grasp  gradu- 
ally and  piecemeal  what  they  are  unable  to  grasp  all 
at  once.  These  auxiliary  conceptions  would  be  de- 
void of  value,  could  we  not  reach,  by  their  help,  the 
graphic  representation  of  the  sense-given  facts. 

When  I  see  in  thought  a  white  beam  of  light  which 
falls  upon  a  prism  issue  forth  in  a  fan-shaped  band  of 
colors  having  certain  angles  which  I  can  specify  be- 
forehand ;  when  I  see  its  real  spectrum-image,  ob- 
tained upon  a  screen  by  interposing  a  lens,  and  in  that 
image,  at  points  determinable  in  advance,  Fraunhofer's 


X5«  THE  ANALYSIS  OF  THE  SENSATIONS. 

lines ;  when  I  see,  in  my  mind,  how  these  self-same 
lines  alter  their  position  on  the  prism  being  turned, 
on  its  substance  being  changed,  or  on  the  thermom- 
eter in  contact  with  it  altering  its  register,  then  I  know 
all  that  I  can  require.  All  auxiliary  conceptions,  laws, 
and  formulae,  are  but  quantitative  norms,  regulating 
my  sensory  representation  of  the  facts.  The  latter  is 
the  endf  the  former  are  the  means. 

6. 

The  adaptation  of  thoughts  to  facts,  accordingly, 
is  the  aim  of  all  scientific  research.  In  this,  science 
only  deliberately  and  consciously  pursues  what  in  daily 
life  goes  on  unnoticed  and  of  its  own  accord.  As  soon 
as  we  become  capable  of  self-observation,  we  find  our 
thoughts,  in  large  measure,  already  adjusted  to  the 
facts.  Our  thoughts  marshal  the  elements  before  us 
in  groups  copying  the  order  of  the  sense-given  facts. 
But  the  limited  supply  of  the  mental  elements  cannot 
keep  pace  with  the  constantly  augmenting  sweep  of 
experience.  Almost  every  new  fact  necessitates  a  new 
adaptation,  which  finds  its  expression  in  the  operation 
known  z.s  judgment. 

This  process  of  judgment  is  easily  followed  in  chil- 
dren. A  child,  on  its  first  visit  from  the  town  to  the 
country,  strays,  for  instance,  into  a  large  meadow, 
looks  about,  and  says  wonderingly  :  **We  are  in  a 
ball.     The  world  is  a  blue  ball."^     Here  we  have  two 

1  This  case  is  not  fictitious,  but  was  observed  in  my  three-year  old  child. 


PHYSICS. 


'57 


judgments.  What  is  the  process  accompanying  their 
formation?  In  the  first  instance,  the  existing  percept 
or  sense-given  image  of  the  company  *'we"  is  broad- 
ened into  a  new  representative  image  by  union  with 
the  similarly  existing  percept  of  a  ball.  Likewise,  in 
the  second  judgment,  the  image  of  the  **  world"  (i.e., 
all  the  objects  of  the  environment)  is  supplemented 
by  combination  with  the  image  of  an  enveloping  blue 
ball  (the  percept  of  which  must  also  have  been  pres- 
ent, since  otherwise  the  name  for  it  would  have  been 
wanting).  A  judgment  is  thus  always  a  supplementing 
or  amendment  of  the  deficiencies  of  a  sensuous  per- 
cept to  represent  completely  a  sensuous  fact.  If  the 
judgment  can  be  expressed  in  words^  then  the  new 
percept  is  never  more  than  a  combination  of  formerly 
established  memory-images,  which  can  also  be  elicited 
in  other  persons  by  words. 

The  process  of  judgment,  therefore,  in  the  present 
case  consists  in  the  enrichment,  extension,  and  sup- 
plementation of  existing  sensuous  percepts  by  other 
existing  sensuous  percepts,  agreeably  to  the  require- 
ments of  definite  sense-given  facts.  If  the  process  is 
over  with,  and  the  image  has  assumed  a  familiar  shape, 
making  its  appearance  in  consciousness  as  a  distinct 
and  intact  product,  then  we  have  no  longer  to  do  with 
a  judgment  but  merely  with  a  phenomenon  of  memory. 
To  the  forming  of  such  *' intuitive  knowledge,"  as 
Locke  calls  it,  natural  science  and  mathematics  mainly 
owe  their  growth.     Consider,  for  example,  the  follow- 


X58  THE  ANALYSIS  OF  THE  SENSATIONS. 

ing  Statements :  (i)  the  tree  has  a  root ;  (2)  the  frog 
has  no  claws  ;  (3)  the  caterpillar  is  transformed  into  a 
butterfly;  (4)  weak  sulphuric  acid  dissolves  zinc ;  (5) 
friction  electrifies  glass ;  (6)  an  electric  current  de- 
flects a  magnetic  needle  ;  (7)  a  cube  has  six  surfaces, 
eight  corners,  twelve  edges.  The  first  statement  em- 
bodies a  spatial  extension  of  the  percept  tree,  the 
second  a  correction  of  a  percept  too  hastily  generalised 
from  habit,  the  third,  fourth,  fifth,  and  sixth  embody 
temporal  extensions  of  their  respective  representa- 
tions. The  seventh  proposition  is  an  example  of  geo- 
metrical **  intuition." 

7. 

Intuitive  knowledge  of  the  sort  just  described,  im- 
presses itself  upon  the  memory  and  makes  its  appear- 
ance there  in  the  form  of  recollections  which  spon- 
taneously supplement  every  fact  presented  by  the 
senses.  But  the  facts  not  being  all  alike,  only  their 
common  elements  are  emphasised,  and  so  we  reach  a 
principle  which  holds  a  paramount  place  in  memory — 
the  principle  of  broadest  possible  generalisation  or  con- 
tinuity. On  the  other  hand,  if  memory  is  to  satisfy 
the  requirements  made  by  the  dissimilarities  of  facts, 
and  be  of  real  practical  use,  it  must  conform  to  the 
principle  of  sufficient  differentiation.  Even  the  animal 
is  reminded,  by  soft,  bright  red  and  yellow  fruits  (seen 
without  exertion  on  the  tree),  of  their  sweet  taste,  and 
by  green  hard  fruits  (which  are  seen  with  difl&culty),  of 


PHYSICS.  159 

their  sour  taste.  The  insect-hunting  monkey  snatches 
at  everything  that  buzzes  and  flies,  but  avoids  the 
yellow  and  black  fly,  the  wasp.  Here  we  have  ex- 
pressed, distinctly  enough,  the  combined  effort  for 
greatest  possible  generalisation  and  continuity  and  for 
practically  sufficient  differentiation  of  memory.  And  both 
ends  are  attained  by  the  same  means,  the  selection  and 
emphasis  of  those  particular  elements  of  the  sensuous  per- 
ception which  are  determinative  of  the  direction  which 
the  thought  must  pursue  to  suit  the  experience.  The 
physicist  proceeds  in  quite  an  analogous  manner,  when 
he  says  (generalising)  :  All  transparent  solids  refract 
incident  light  towards  the  perpendicular,  and  when  he 
adds  (differentiating)  :  amorphous  bodies  and  isomeric 
crystals  simply,  the  rest  doubly. 

8. 

A  considerable  portion  of  mental  adaptation  takes 
place  unconsciously  and  involuntarily,  under  the  nat- 
ural guidance  of  the  facts  presented  to  the  senses.  If 
this  adaptation  has  become  sufiiciently  comprehensive 
to  embrace  the  vast  majority  of  the  occurring  facts, 
and  subsequently  we  come  upon  a  fact  which  runs  vio- 
lently counter  to  the  customary  course  of  our  thought 
without  our  being  able  to  discover  at  once  the  deter- 
minative factor  likely  to  lead  to  a  new  differentiation, 
then  a  problem  arises.  The  new,  unusual,  and  marvel- 
lous acts  as  a  stimulus,  which  irresistibly  attracts  the 
attention.     Practical  considerations,  or  even  bare  in- 


z6o  THE  ANALYSIS  OF  THE  SENSATIONS. 

tellectual  discomfort,  may  engender  a  volitional  frame 
of  mind  requiring  the  removal  of  the  contradiction,  or 
a  consequent  new  mental  adaptation.  Thus  arises 
purposive  thought-adaptation,  investigation. 

For  example,  we  have  all,  at  some  time  or  another, 
quite  contrary  to  the  common  run  of  our  experience, 
observed  a  lever  or  pulley  lifting  by  means  of  a  small 
weight  a  large  weight.  We  seek  the  differentiating 
factor,  which  in  the  sensuous  phenomenon  itself  is  not 
immediately  given.  We  compare  a  number  of  different 
instances  falling  under  the  same  category,  note  the 
varying  influences  exerted  by  the  weights  and  the  arms 
of  the  lever,  and  then,  only  after  having  mastered  by 
strenuous  independent  efforts  of  our  reasoning  powers 
the  abstract  conceptions  of  ** moment"  and  '*work," 
do  we  reach  the  satisfactory  solution  of  the  problem. 
''Moment"  or  **work"  is  the  differentiating  element. 
The  noting  of  the  factors  '* moment"  or  "work"  hav- 
ing become  a  mental  habitude,  the  problem  no  longer 
exists. 

9- 

What  do  we  do  when  we  abstract  ?  What  is  an 
abstraction  ?  What  is  a  concept  ?  Is  there  a  sensu- 
ous image  corresponding  to  every  concept  ?  I  cannot 
represent  to  myself  a  general  man.  I  can  at  most  rep- 
resent to  myself  a  particular  man,  or  perhaps  one  com- 
bining such  accidental  peculiarities  of  different  men  as 
are  not  exclusive  of  each  other.     A  general  triangle, 


PHYSICS.  i6i 

which  is  at  once  right-angled  and  equilateral,  cannot 
be  imagined.  Further,  the  image  thus  rising  into  con- 
sciousness at  the  name  of  the  concept,  and  accompany- 
ing the  conceptual  process,  is  not  the  concept.  In 
fact,  generally,  words,  being  designations  which  from 
necessity  must  be  used  to  describe  many  different  per- 
cepts, are  far  from  being  identical  with  concepts.  A 
child  who  has  seen  for  the  first  time  a  black  dog  and 
heard  it  named,  soon  afterward  calls  a  large  and 
swiftly-running  black  beetle,  **dog";  or  a  pig  or  a 
sheep,  **dog."^  Any  similarity  whatever  reminding 
him  of  the  first-named  percept  naturally  leads  to  the 
use  of  its  name.  The  point  of  similarity  need  not 
be  at  all  the  same  in  the  successive  cases.  It  may 
reside,  for  instance,  in  one  case  in  the  color,  again  in 
the  motion,  then  in  the  form,  then  in  the  external  cov- 
ering ;  and  so  on.  Of  a  concept  there  is  no  question. 
Thus,  a  child  calls  the  feathers  of  a  bird  '* hairs"; 
the  horns  of  a  cow  '< feelers";  a  brush,  the  beard  of 
its  father,  and  the  down  of  a  dandelion,  without  dis- 
tinction, a  *'brush";  and  so  on.^  Most  adults  treat 
words  in  the  same  manner,  only  less  noticeably  so, 
because  they  have  a  larger  vocabulary  at  their  dis- 
posal. The  illiterate  man  calls  a  rectangle  a  square, 
and  occasionally,  too,  a  cube,  a  square,  because  of  its 
rectangular  boundaries.   The  science  of  language,  and 

1  Thus  the  Marcomanni  called  the  lions  sent  across  the  Danube  by  the 
Romans  "dogs,"  and  the  lonians  called  the  x^F^^'-  °^  *^^  Nile  from  the 
lizards  of  their  native  underbrush,  "  crocodiles."     (Herodotus,  II.,  69.) 

2  All  these  examples  are  taken  from  experience. 


x62  THE  ANALYSIS  OF  THE  SENSATIONS. 

a  number  of  authenticated  historical  examples,  show 
that  even  nations  do  not  act  differently.^ 

A  concept  is  never  a  finished  percept.  In  using  a 
word  denoting  a  concept,  there  is  nothing  involved  in 
the  word  but  a  simple  impulse  to  perform  some  famil- 
iar sensory  operation^  as  the  result  of  which  a  defi- 
nite sensuous  element  (the  mark  of  the  concept)  is 
obtained.  For  example,  when  I  think  of  the  concept 
''heptagon,"  I  enumerate  the  angles  of  a  figure  visi- 
bly before  me  or  of  its  image  in  my  consciousness ; 
and  when  in  so  doing  I  reach  seven,  in  which  case  the 
sound,  the  numeral,  or  my  finger  announces  the  sensu- 
ous mark,  then  by  this  very  act  the  given  percept  falls 
under  the  given  concept.  In  speaking  of  a  * 'square 
number,"  I  seek  to  resolve  the  number  given  into 
components  typified  by  the  operation  SV^S^  6x6,  etc., 
the  sensuous  characteristic  of  which,  being  the  equal- 
ity of  the  two  factors  multiplied,  is  patent.  The  same 
holds  good  of  every  concept.  The  sensuous  activity 
excited  by  the  word  may  be  made  up  of  a  number 
of  operations,  one  of  which  may  involve  the  other. 
But  the  result  is  always  a  sensuous  element  not  before 
present. 

In  looking  at  or  in  imagining  a  heptagon,  the  fact 
of  its  having  seven  angles  need  not  be  present  to  my 
mind.  This  fact  is  distinctly  cognised  only  on  count- 
ing. Frequently,  the  new  sensuous  element  may  be 
so  obvious  (as  it  is,  for  instance,  in  the  case  of  the 

ISee  Whitney,  Life  and  Growth  of  Language. 


PHYSICS.  163 

triangle)  that  the  operation  of  counting  seems  un- 
necessary. Such  cases,  however,  are  exceptional,  and 
constitute  the  main  source  of  misunderstandings  con- 
cerning the  nature  of  concepts.  I  do  not  directly  see, 
by  an  act  of  sight,  in  the  case  of  conic  sections  (the 
ellipse,  parabola,  hyperbola)  that  these  curves  may 
be  all  subsumed  under  the  same  concept ;  but  I  can 
discover  the  fact  by  cutting  a  cone,  and  by  construct- 
ing the  equation  for  conies. 

When,  therefore,  we  apply  abstract  concepts  to  a 
fact,  the  fact  merely  acts  upon  us  as  an  impulse  to  per- 
form a  definite  operation  of  the  senses,  which  opera- 
tion introduces  new  sensuous  elements,  determining 
the  subsequent  course  of  our  thought  with  reference 
to  the  fact.  By  this  activity  we  enrich  and  extend  the 
fact,  which  before  was  too  meagre  for  us.  We  do 
what  the  chemist  does  with  his  colorless  solution  of 
salts,  when  by  a  given  operation  he  obtains  from  it  a 
yellow  or  brown  precipitate,  having  the  power  to  dif- 
ferentiate the  career  of  his  thought.  The  concept  of 
the  physicist  is  a  precise  and  definite  reaction-activity , 
which  enriches  a  fact  with  new  sensuous  elements. 

10. 

To  revert  to  an  earlier  example,  when  we  behold 
a  lever,  we  are  impelled  to  measure  the  length  of 
its  arms,  to  weigh  its  weights,  and  to  multiply  the 
numbers  representing  the  lengths  of  its  arms  by  the 
numbers   representing  the  values  of  its  weights.     If 


1 64  THE  ANALYSIS  OF  THE  SENSATIONS. 

the  same  sensuous  numerical  symbol  corresponds  to 
both  products,  we  expect  equilibrium.  We  have  here 
gained  a  new  sensuous  element  which  was  not  an- 
tecedently given  in  the  bare  fact  itself,  but  which 
now  differentiates  the  career  of  our  thought.  If  we 
will  keep  well  in  mind  that  thought  by  concepts  is  a 
reaction-activity  which  must  be  thoroughly  practised, 
we  shall  understand  the  well-known  fact  that  no  one 
can  familiarise  himself  with  mathematics  or  physics 
or  with  any  natural  science  by  mere  reading  without 
practical  exercise.  Comprehension  here  depends  en- 
tirely on  action.  In  fact,  it  is  impossible  in  any  prov- 
ince to  grasp  the  higher  abstractions  without  a  prac- 
tical working  knowledge  of  its  details. 

Facts  then  are  extended  and  enriched,  and  ulti- 
mately again  simplified  by  the  action  of  concepts. 
For,  when  the  new  determinative  sensuous  element 
is  found  (say,  the  number  representing  the  virtual 
moments  of  the  lever),  then  this  alone  is  investigated, 
and  the  most  diverse  groups  of  facts  are  found  to 
resemble  and  not  to  resemble  each  other  solely  by 
virtue  of  this  element.  Thus  here  also,  as  in  the  case 
of  intuitive  knowledge  above  mentioned,  everything 
is  reducible  to  the  discovery,  selection,  and  emphasis 
of  the  determinative  sensuous  elements.  Investigation 
here  only  reaches  by  a  roundabout  way  what  is  imme- 
diately presented  to  intuitive  cognition. 

The  chemist  with  his  reactions,  the  physicist  with 
his  measuring  rod,  scales,  and  galvanometer,  and  the 


PHYSICS.  165 

mathematician,  all  treat  facts  in  quite  the  same  way ; 
the  only  difference  being  that  the  latter  needs  to  go 
least  outside  of  the  elements  ajiy  .  .  .  K LM  in  his 
extension  of  facts.  The  aids  of  the  mathematician  are 
always  conveniently  at  hand.  The  investigator  and 
all  his  thought  are  a  fragment  only  of  nature,  like 
everything  else.  A  real  chasm  between  him  and  other 
parts  'does  not  exist.     All  elements  are  equivalent. 

On  the  preceding  theory,  the  essence  of  abstrac- 
tion is  not  exhausted  by  terming  it  (with  Kant)  nega- 
tive attention.  It  is  true  that,  in  abstracting,  the  at- 
tention is  turned  away  from  many  sensuous  elements, 
but  on  the  other  hand,  it  is  turned  toward  other  and 
new  sensuous  elements ;  and  precisely  this  latter  fact 
is  the  essential  feature.  Every  abstraction  is  founded 
on  the  prominence  given  to  certain  sensuous  elements. 

II. 

The  facts  given  by  the  senses,  therefore,  are  alike 
the  starting-point  and  the  goal  of  all  the  mental  adap- 
tations of  the  physicist.  The  thoughts  which  follow 
the  sense-given  fact  immediately  are  the  most  famil- 
iar, the  strongest,  and  the  most  intuitive.  Where  we 
cannot  at  once  follow  a  new  fact,  the  strongest  and 
most  familiar  thoughts  press  forward  to  lend  to  it 
their  richer  and  preciser  moulds.  This  process  is  the 
source  of  every  hypothesis  and  speculation  in  science, 
which  latter  all  find  their  warrant  in  the  mental  adap- 
tation that  has  developed  and  ultimately  given  them 


i66  THE  ANALYSIS  OF  THE  SENSATIONS. 

birth.  Thus  we  think  of  the  planets  as  projectiles, 
figure  to  ourselves  an  electric  body  as  covered  with 
a  fluid  that  acts  at  a  distance,  think  of  heat  as  a  sub- 
stance that  passes  from  one  body  to  another,  until 
finally  the  new  facts  become  as  familiar  and  as  intui- 
tive as  the  older  ones,  which  we  had  used  as  mental 
helps.  Even  where  immediate  intuition  is  out  of  the 
question,  the  thoughts  of  the  physicist,  by  carefully 
observing  the  principle  of  continuity  and  of  sufficient 
differentiation,  become  ordered  in  an  economically  as- 
sorted system  of  conceptual  reactions,  which  lead,  at 
least  by  the  shortest  path,  to  intuitive  knowledge. 

12. 

Let  us  now  consider  the  results  of  mental  adapta- 
tion. Thoughts  can  adapt  themselves  only  to  what  is 
constant  in  the  facts ;  the  mental  reconstruction  of  con- 
stant elements  alone  can  yield  advantage  in  point  of 
economy.  Herein  is  contained  the  ultimate  ground 
of  our  effort  for  continuity  in  thought,  that  is,  for  the 
preservation  of  the  greatest  possible  constancy,  and 
by  it,  too,  the  results  of  the  adaptation  are  rendered 
intelligible.* 

13- 

The  unconditionally  constant  we  term  substance. 
I  see  a  body  upon  turning  my  eyes  in  its  direction.  I 
can  see  it  without  touching  it,  I  can  touch  it  without 

i  Compare  nay  Mechanics,  Eng  trans.,  Chicago,  1893,  p.  504. 


PHYSICS.  167 

seeing  it.  Although  thus  the  actual  appearance  of  the 
component  elements  of  the  complex  is  joined  to  con- 
ditions, I  yet  have  these  conditions  too  absolutely  in 
my  hands  to  appreciate  or  notice  them  markedly.  I 
regard  the  body,  or  the  complex  of  elements,  or  the 
nucleus  of  this  complex,  as  always  present,  whether, 
for  the  moment,  it  is  the  object  of  my  senses  or  not. 
Having  always  ready  the  thought  of  this  complex,  or, 
symbolically,  the  thought  of  its  nucleus,  I  gain  the 
advantage  of  being  able  to  predict,  and  avoid  the  dis- 
advantage of  ever  being  surprised.  My  behavior  is 
the  same  with  regard  to  the  chemical  elements,  which 
also  appear  to  me  unconditionally  constant.  Although 
here  my  mere  willing  it  is  not  sufficient  to  make  of  the 
complexes  in  question  sensuous  facts,  and  although  in 
the  present  case  outward  aids  also  are  necessary,  I 
yet  leave  these  aids  out  of  account  as  soon  as  they 
have  become  familiar  to  me,  and  look  upon  the  chem- 
ical elements  throughout  as  constant.  The  man  who 
believes  in  atoms  does  the  same  with  these  auxiliary 
notions. 

In  the  same  manner  as  with  the  complex  of  ele- 
ments corresponding  to  a  body,  we  may  also  proceed, 
on  a  higher  plane  of  thought-adaptation,  with  entire 
provinces  of  facts.  In  speaking  of  electricity,  mag- 
netism, light,  and  heat,  even  when  not  associating 
substances  with  these  names,  we  yet  ascribe  constancy 
to  these  provinces  of  facts,  leaving  entirely  out  of  ac- 
count the  familiar  conditions   under  which   they  ap- 


i68  THE  ANAL  YSIS  OF  THE  SENS  A  TIONS. 

pear ;  and  we  hold  the  ideas  which  reproduce  them 
always  in  readiness,  thereby  gaining  an  advantage 
similar  to  that  explained  above.  When  I  say  a  body 
is  *' electric,"  far  more  memories  arise  in  my  mind, 
and  my  expectations  are  associated  with  far  more 
definite  groups  of  facts,  than  if  I  had  emphasised,  for 
instance,  the  attractions  displayed  in  the  single  cases. 
Yet  this  hypostasising  may  have  its  disadvantages,  also. 
In  the  first  place,  in  proceeding  thus,  we  always  follow 
the  same  historical  paths.  It  may  be  important,  how- 
ever, to  recognise  that  there  is  no  such  thing  as  a  spe- 
cific electrical  fact,  that  every  such  fact  can  just  as 
well  be  regarded,  for  example,  as  a  chemical  one,  or 
as  a  thermal  one,  or  rather  that  all  physical  facts  are 
made  up,  in  an  ultimate  analysis,  of  the  same  sensu- 
ous elements  (colors,  pressures,  spaces,  times),  and 
that  we  are  merely  reminded  by  the  term  ** electric" 
of  that  particular  form  in  which  we  first  became  ac- 
quainted with  the  fact. 

If  we  have  once  accustomed  ourselves  to  regard 
the  body,  to  and  from  which  we  can,  at  pleasure,  turn 
our  glance  and  touching  hand,  as  constant,  then  it  is 
easy  for  us  to  do  the  same  in  cases  in  which  the  con- 
ditions of  sensuous  manifestation  lie  entirely  without 
our  reach — for  example,  in  the  case  of  the  sun  and 
moon,  which  we  cannot  touch,  or  of  parts  of  the  world 
which  we  have  seen  but  once  and  shall  perhaps  never 
see  again,  or  that  we  know  only  by  description.  Such 
a  method  of  procedure  may  have  a  high  importance 


PHYSICS.  169 

in  an  undisturbed  and  economical  conception  of  the 
world,  but  it  is  certainly  not  the  only  legitimate 
method.  It  would  be  merely  a  consistent  additional 
step,  if  we  were  to  regard  the  whole  past,  which  is, 
indeed,  still  present  in  its  vestiges  (since,  for  instance, 
we  see  the  stars  where  they  were  thousands  of  years 
ago)  and  the  whole  future,  which  is  present  in  germ 
(since,  for  example,  our  solar  system  will  be  seen 
where  it  now  is,  thousands  of  years  hence)  as  con- 
stant. The  entire  passage  of  time,  in  fact,  is  dependent 
solely  on  conditions  of  sensuous  activity.  Were  a 
special  purpose  given,  even  this  step  might  be  haz- 
arded. 

14. 

Really  unconditioned  constancy  does  not  exist,  as 
will  be  evident  from  the  preceding  considerations. 
We  attain  to  the  idea  of  absolute  constancy  only  as 
we  overlook  or  underrate  conditions,  or  as  we  regard 
them  as  always  given,  or  as  we  deliberately  disregard 
them.  There  is  but  one  sort  of  constancy,  which  em- 
braces all  forms,  namely,  constancy  of  connexion  (or 
of  relation). 

The  majority  of  the  propositions  of  natural  science 
express  such  constancies  of  connexion  :  **  The  tadpole 
is  metamorphosed  into  a  frog  ;  chlorate  of  sodium 
makes  its  appearance  in  the  form  of  cubes-  Rays  of 
light  are  rectilinear.  Bodies  fall  with  an  acceleration 
of  9-81  {m/sec^)."     When  these  constancies  are  ex- 


17©  THE  ANALYSIS  OF  THE  SENSATIONS. 

pressed  in  concepts,  we  call  them  laws.  Force  (in 
the  mechanical  signification")  is  likewise  merely  a  con- 
stancy of  connexion.  When  I  say  that  a  body  A  ex- 
erts a  force  on  a  body  B,  I  mean  that  B,  on  coming 
into  contraposition  with  A^  is  immediately  affected 
by  a  certain  acceleration  with  respect  to  A. 

The  singular  illusion,  that  the  substance  A  is  the 
absolutely  constant  vehicle  of  a  force  which  takes  effect 
immediately  on  B's  being  contraposed  to  A^  is  easily 
shattered.  If  we,  or  more  exactly  speaking,  our  sense- 
organs,  be  put  in  the  place  of  B,  here  a  condition  in- 
tervenes, which,  seeing  that  it  is  possible  at  any  time 
to  fulfil  it,  is  invariably  disregarded,  and  thus  A  ap- 
pears to  us  absolutely  constant.  Similarly,  a  magnet, 
which  we  see  as  often  as  we  care  to  look  in  its  direc- 
tion, appears  to  us  the  constant  vehicle  of  a  mag- 
netic force,  which  becomes  operative  only  upon  being 
brought  near  to  a  particle  of  iron,  which  we  cannot 
disregard  as  easily  as  ourselves  without  noticing  the 
fact.^  The  phrases,  "No  matter  without  force,  no 
force  without  matter,"  which  are  but  abortive  attempts 
to  remove  a  self-incurred  contradiction,  become  su- 
perfluous on  our  recognising  only  constancies  of  con- 
nexion, 

iTo  the  child  everything  appears  substantial,  for  perceiving  which  only 
his  senses  are  necessary.  The  child  asks  where  the  shadow,  where  the  extin- 
guished light  goes  to.  He  will  not  suffer  the  electrical  machine  to  be  turned 
any  great  length  of  time  for  fear  of  exhausting  the  supply  of  sparks,  etc.— 
Only  upon  noting  conditions  of  a  fact  that  are  outside  ourselves  does  the  im- 
pression of  substantiality  disappear.  The  history  of  the  theory  of  heat  is 
very  instructive  in  this  connexion. 


J^HYSICS.  171 


15- 


Given  a  sufficient  constancy  of  environment,  there 
is  developed  a  corresponding  constancy  of  thought. 
By  virtue  of  this  constancy  our  thoughts  are  spon- 
taneously impelled  to  complete  all  incompletely  ob- 
served facts.  The  impulse  in  question  is  not  prompted 
by  the  individual  facts  as  observed  at  the  time  ;  nor 
is  it  intentionally  evoked  ;  but  we  find  it  operative  in 
ourselves  entirely  without  our  personal  intervention. 
It  confronts  us  like  a  power  from  without^  yet  as  a 
power  which  continually  accompanies  and  assists  us, 
as  a  thing  of  which  we  stand  in  need,  in  order  to  sup- 
ply the  deficiencies  of  the  fact.  Although  it  is  devel- 
oped by  experience,  it  contains  more  than  is  contained 
in  the  single  experience.  The  impulse  in  a  certain 
measure  enriches  the  single  fact  Through  it  the  latter 
is  more  to  us.  By  this  impulse  we  have  always  a  larger 
portion  of  nature  in  our  field  of  vision  than  the  inex- 
perienced man  has,  with  the  single  fact  alone.  For 
the  human  being,  with  his  thoughts  and  his  impulses, 
is  himself  merely  a  piece  of  nature,  which  is  added  to 
the  single  fact.  This  impulse,  however,  can  lay  no 
claim  to  infallibility,  and  there  exists  no  necessity 
compelling  the  facts  to  correspond  to  it.  Our  con- 
fidence in  it  rests  entirely  upon  the  supposition,  which 
has  been  substantiated  by  numerous  trials,  of  the  suf- 
ficiency  of   the   mental    adaptation, — a   supposition. 


172  THE  ANALYSIS  OF  THE  SENSATIONS, 

however,  which  must  be  prepared  to  be  contradicted 
at  any  moment. 

Not  all  our  ideas  representing  facts  have  the  same 
constancy.  Whenever  we  have  a  special  interest  in 
the  representation  of  facts,  we  endeavor  to  support 
and  corroborate  ideas  of  lesser  constancy  by  ideas  of 
greater  constancy,  or  to  replace  them  by  the  latter. 
Thus  Newton  conceived  the  planets  as  projectiles, 
although  Kepler's  laws  were  already  well  known,  the 
tides  as  attracted  by  the  moon,  although  the  facts  of 
their  movement  had  long  been  ascertained.  We  be- 
lieve we  understand  the  suction  of  a  pump,  the  flowing 
of  a  siphon,  only  as  we  add  in  thought  the  pressure 
of  the  air.  Similarly  we  seek  to  conceive  electrical, 
optical,  and  thermal  processes  as  mechanical  proces- 
ses. This  need  of  the  support  of  weaker  thoughts  by 
stronger  thoughts  is  also  called  the  need  of  causality, 
and  is  the  moving  spring  of  all  explanation  in  science. 
We  naturally  prefer,  as  the  foundation  of  this  process, 
the  strongest  and  most  thoroughly  tested  thoughts, 
and  these  are  given  us  by  our  much  exercised  mechan- 
ical functions,  which  we  may  test  anew  at  any  moment 
without  many  or  cumbersome  appliances.  Hence  the 
authority  of  mechanical  explanations,  especially  those 
by  pressure  and  impact.  A  corresponding  and  still 
higher  authority  attaches  to  mathematical  thoughts, 
for  in  their  development  we  stand  in  need  of  no  ex- 
traneous means  whatever,  but  on  the  contrary,  in- 
variably carry  most  of  the  material  for  experimenting 


PHYSICS,  173 

about  with  us.  But  if  we  are  once  apprised  of  this, 
the  need  of  mechanical  explanations  is  appreciably 
weakened.^ 

It  was  said  above  that  man  himself  is  a  fragment 
of  nature.  Let  me  illustrate  this  by  an  example.  For 
the  chemist  a  substance  may  be  sufficiently  character- 
ised merely  by  his  sensations.  In  this  case  the  chem- 
ist himself  supplies,  by  inner  means,  the  whole  wealth 
of  fact  necessary  to  the  determination  of  his  course  of 
thought.  But  in  other  cases,  resources  to  reaction  by 
the  help  of  outward  means  may  be  necessary.  When 
an  electric  current  flows  round  a  magnetic  needle  situ- 
ated in  its  plane,  the  north  pole  of  the  needle  is  de- 
flected to  my  left  if  I  imagine  myself  as  Ampere's 
swimmer  in  the  current.  I  enrich  the  fact  (current 
and  needle)  which  is  insufficient  in  itself  to  define 
the  direction  of  my  thought,  by  introducing  myself 
into  the  experiment  by  an  inner  reaction.  I  may  like- 
wise lay  tny  watch  in  the  plane  of  the  circuit,  so  that 
the  hand  moves  in  the  direction  of  the  current.  Then 
the  south  pole  falls  in  front  of,  the  north  pole  behind 
the  dial.  Or  I  may  make  of  the  circuit  traversed  by 
the  current  a  sun-dial  (on  the  plan  of  which  the  watch 

1  Physical  experiences  other  than  mechanical  may  approach  to  the  value 
of  mechanical  experiences  as  they  become  more  familiar.  In  my  opinion 
Strieker  has  advanced  a  correct  and  important  view  in  bringing  causality 
into  connexion  with  the  will.  When  I  was  a  young  decent,  I  myself  advocated 
with  great  warmth  and  onesidedness  (in  the  exposition  of  Mill's  method  of 
difference)  the  view  expressed  by  Strieker.  And  the  idea  has  never  quite  left 
me  (comp.,  for  example,  my  Science  of  Mechanics,  Eng.  trans.,  pp.  84,  304,  485.) 
However,  I  am  at  present  of  the  opinion,  as  the  above  discussion  shows,  that 
this  question  is  not  so  simple  and  must  be  looked  at  from  several  sides. 


174  "^HE  ANALYSIS  OF  THE  SENSATIONS. 

in  fact  was  modelled),  so  arranging  it  that  the  shadow 
follows  the  current.  In  this  case  the  north  pole  will 
move  towards  the  shadowed  side  of  the  plane  of  the 
current.  The  two  last-mentioned  reactions  are  out- 
ward reactions.  The  two  species  of  reactions  could 
not  be  made  use  of  indiscriminately  if  a  chasm  existed 
between  myself  and  the  world.  Nature  is  a  single 
whole.  The  fact  that  the  two  species  of  reaction  are 
not  known  in  all  cases,  and  that  frequently  the  ob- 
server appears  to  be  entirely  without  influence,  proves 
nothing  against  the  view  advanced. 

1 6. 

Whenever  it  happens,  in  a  complexus  of  elements, 
that  some  of  the  elements  get  replaced  by  others, 
necessarily  the  constancy  of  the  connexion  is  cha?iged. 
In  such  cases  it  is  desirable  to  discover  a  constancy 
which  survives  this  change.  J.  R.  Mayer  first  felt 
this  need,  and  satisfied  it  by  enunciating  his  concept 
of  "  force, "  which  corresponds  to  the  technical  me- 
chanical concept  of  **work"  (Poncelet)  or  more  ex- 
actly to  the  more  general  concept  of  "energy."  Mayer 
conceives  this  force  (or  energy)  as  something  abso- 
lutely constant  (as  a  store  of  something,  as  a  sub- 
stance), and  so  goes  back  to  the  strongest  and  most 
intuitive  thoughts.  We  perceive,  from  Mayer's  strug- 
gle with  expressions,  with  general  philosophical 
phrases,  etc.  (noticeable  in  the  first  and  second  of  his 
treatises),  that  he  at  first  felt  instinctively  and  intuitively 


(.■ 


PHYSICS,  175 

the  urgent  need  of  such  a  concept.  But  the  great 
achievement  was  accomplished  only  upon  his  adapting 
the  existing  physical  concepts  to  the  requirements  of 
the  facts  and  his  needs.  ^ 

1  In  observing  a  freely  falling  body,  we  note  the  constancy  v=VTgli,  which 
we  may  also,  if  we  like,  express  in  the  torra  g- h=vi I2.  Making  the  entire 
possible  distance  of  descent  H^h+h',  then  also  gh'-\-  vi/2  =  const.  We  may 
now  imagine  a  constant  stock  of  something  (figuratively  a  sub- 
stance) which,  when  the  event  occurs,  is  converted  from  the 
form^A'  into  the  form  z'2/2,  or  ii ph'-\-mv2  fz  be  made  constant, 
from  the  form  pk'  into  the  form  ntv^lz,  but  which  always  pre-  H  ■ 
serves  its  total  value  unchanged.  Such  a  conception  is  well 
qualified  to  meet  our  needs  and  to  turn  our  thoughts  into  famil- 
iar channels.  Nevertheless,  there  is  nothing  compelling  us  to 
regard  gh  and  vt/z  as  equivalent.  In  the  first  equation  v=Vzgh,  there  is  no 
perceptible  trace  of  such  a  conception.  If  it  be  found,  however,  that,  when 
mv2/2  disappears /A'  may  reappear  (for  instance,  in  the  rebound  of  an  elastic 
ball),  then  this  conception  serves  a  highly  practical  purpose.  (Comp.  Mach, 
Erhaltungder  Arbeit,  p.  45,  and  for  many  instructive  discussions  of  particu- 
lars, the  admirable  work  of  J.  Popper,  Die  physikalischen  GrundsStze  der 
electrischen  KraftUbertragung.) 

If  the  body  does  not  fall  freely,  but  in  gradually  sinking  heats  another 
body  or  renders  it  electric,  then  an  entirely  new  constancy  takes  the  place  of 
the  first.  Nothing  compels  us  to  regard  the  quantity  of  heat  generated  or  the 
electric  potential  produced  as  the  equivalent  of  the  missing  rnv^/z.  Our  de- 
termining that  the  heat  shall  stand  /or  exactly  as  muck  as  the  corresponding 
fh'  is  arbitrary,  notwithstanding  its  great  convenience.  It  was  primarily 
Mayer's  need  that  led  him  to  write  down  his  equation,  which  as  regards  the 
facts  was  not  as  yet  satisfied  and  which  is  generally  incorrect  if  the  right 
units  are  not  selected. 

Facts  can  teach  us  constancy  of  connexion  only.  In  reversible  processes 
(processes  that  are  independent  of  time)  we  find,  periodic  changes  of  elements 
connected  with  periodic  changes  of  other  elements,  simply.  There  is  nothing 
in  this  of  equivalence.  Heat  may  take  the  place  oiph',  and  in  place  of  this 
again  the  same  ph'  may  reappear.  This  gives  the  conception /racZ/Va/  value. 
With  reference  to  changes  which  are  not  reversible  (changes  dependent  on 
time)  the  conception  of  equivalence  is  idle.  Whether  or  not  heat  which  can 
no  longer  reappear  as  work  may  still  be  regarded  as  the  equivalent  of  work, 
is  of  no  consequence.  We  might  be  struck  by  i}s\&  proportionality  between /A 
and  quantity  of  heat,  and  think  that  this  certainly  could  not  depend  upon  an 
arbitrary  conception  but  must  inhere  in  nature.  Yet  if  we  had  attempted, 
say,  to  regard  ph  and  quantity  of  electricity  as  equivalent,  this  conception 
would  have  proved  unserviceable,  and  the  idea  would  necessarily  have  re- 
quired modification  until  energy  had  been  substituted  for  quantity  of  elec- 
tricity. That  quantity  of  heat  was  so  readily  offered  in  the  inquiry,  was  a 
fortunate  historical  circumstance,  which  militates  in  no  wise  against  the  cor- 
rectness of  our  considerations.— Mayer's  unusually  powerful  intellectual  in- 


176  THE  ANALYSIS  OF  THE  SENSATIONS. 


17. 

Upon  sufficient  adaptation,  the  facts  are  spontane- 
ously reproduced  by  the  thoughts,  and  incompletely 
given  facts  are  completed.  Physics  can  act  only  as  a 
quantitative  norm  regulating  and  giving  a  raoxo.  precise 
conformation  to  the  spontaneously  flowing  thoughts, 
suitably  to  definite  practical  or  scientific  needs.  When 
I  see  a  body  thrown  horizontally,  the  vivid  picture  of 
a  projectile  in  motion  rises  before  my  mind.  But  the 
artilleryman  or  the  physicist  requires  more.  He  must 
know,  for  example,  that  if  on  applying  the  measuring- 
rod  M  to  the  horizontal  abscissae  of  the  projectile's 
path,  he  can  cou7it  to  i,  2,  3,  4  ...  .  he  must,  on  ap- 
plying the  measure  M*  to  the  vertical  ordinates,  also 
count  to  I,  4,  9,  i6  .  .  .  .  in  order  to  reach  a  point  of 
the  path.  The  function  of  physics  consists,  therefore, 
in  teaching  that  a  fact  which,  on  a  definite  reaction  R 
yields  a  sensory  mark  Ey  also  yields,  on  the  giving  of 
a  different  reaction  R' y  a  second  sensory  mark  E'.  By 
this  means  it  is  possible  to  supply  more  exactly  the 
deficiencies  of  incompletely  given  facts. 

stinct  combined  with  strength  of  conceptual  thought,  his  broad,  comprehen- 
sive vision,  the  clearness  with  which  he  ultimately  determined  the  mechan- 
ical equivalent  of  heat  without  resorting  to  a  new  experiment,  characterises 
him  as  an  investigator  of  the  first  rank.  But  it  by  no  means  follows  from 
this  fact,  that  those  inquirers  who  came  after  him  were  dishonest.  On  the 
contrary,  I  am  convinced,  from  all  the  evidence  accessible  to  me,  that  the 
investigators  in  question  all  followed  independent  courses  of  reasoning, — a 
conclusion  that  I  cannot  further  discuss  here. 


PHYSICS.  177 

i8. 

The  space  of  the  geometrician  Is  by  no  means  made 
up  wholly  of  the  system  of  s-pdice-sensations  (pi  the 
senses  of  sight  and  touch),  but  consists  rather  of  a 
large  body  oi  physical  observations,  having  the  space- 
sensations  as  their  point  of  departure.  In  the  very 
fact  of  the  geometrician's  regarding  his  space  as  con- 
stituted at  all  points  and  in  all  directions  alike,  he 
goes  far  beyond  the  space  given  by  sight  and  touch, 
which  by  no  means  possesses  this  simple  property 
(p.  80).  Without  experience  \n  physics  the  geometri- 
cian would  never  have  reached  this  conception.  The 
fundamental  propositions  of  geometry  have,  as  a  fact, 
been  acquired  wholly  by  means  of  physical  observa- 
tions, by  the  superposition  of  measures  of  length  and 
of  angles,  by  the  application  of  rigid  bodies  to  one  an- 
other. Without  propositions  of  congruence^  no  geom- 
etry. Apart  from  the  fact  that  spatial  images  would 
never  have  been  produced  in  us  without  physical  ex- 
perience, we  should,  even  granting  their  existence, 
never  have  been  able  to  apply  them  to  one  another 
and  to  test  their  congruence,  without  this  knowledge. 
When  we  feel  compelled  to  imagine  an  isosceles  triangle 
as  having  equal  angles  at  its  base,  our  compulsion  is 
due  to  the  remembrance  of  powerful  past  experiences. 
If  the  proposition  had  its  source  in  "pure  intuition," 
there  would  be  no  necessity  for  learning  it.^     That 

IThe  method  of  Euclid  is  undoubtedly  excellent  for  the  instruction  of 
adult  persons,  with  abundant  geometric  experience.    It  serves  to  protect  us 


178  THE  ANALYSIS  OF  THE  SENSATIONS. 

discoveries  may  be  made  by  sheer  power  of  geometrical 
imagination,  and  are  made  so  daily,  merely  proves 
that  the  memory  of  a  given  experience  can  reveal  to 
the  mind  features  which  in  the  original  observation 
escaped  unnoticed ;  just  as  in  the  after-image  of  a 
brightly-lighted  lamp,  new  and  previously  unseen  de- 
tails may  be  discovered.  Even  the  theory  of  numbers 
must  be  looked  at  in  some  such  manner ;  its  funda- 
mental propositions  can  hardly  be  viewed  as  entirely 
independent  of  physical  experience. 

The  cogency  of  geometry  (and  of  all  mathematics) 
is  due,  not  to  the  fact  that  its  theories  are  arrived  at 
by  some  select  and  special  kind  of  cognition,  but  only 
to  the  fact  that  the  empirical  material  which  is  at  its 
base  is  particularly  convenient  and  handy,  has  been  put 
to  the  test  an  untold  number  of  times,  and  can  be  sub- 
jected again  at  any  moment  to  the  same  tests.  More- 
over, the  province  of  space-experience  is  far  more 
limited  than  that  of  the  whole  of  experience.  The 
conviction  of  having  essentially  exhausted  this  limited 
province  soon  arises  and  produces  the  necessary  self- 
confidence. 

A  self-confidence  similar  to  that  of  the  geometri- 
cian is  doubtless  also  possessed  by  the  composer  and 
the  decorative  painter,  who  have  both  gained,  the 
former  in  the  domain  of  sensations  of  tone,  the  latter 

from  the  possible  errors  which  we  have  acquired.  That  no  worse  results 
have  been  entailed  by  use  of  this  method  in  instructing  the  youth  is  due 
entirely  to  the  fact  that  nobody  comes  into  the  hands  of  a  teacher  altogether 
without  geometrical  experience. 


PHYSICS,  179 

in  that  of  sensations  of  color,  a  broad  and  rich  ex- 
perience. To  the  one  no  space-figure  will  occur  the 
elements  of  which  are  not  well  known  to  him,  and  the 
two  others  will  meet  with  no  new  combinations  of  tone 
or  of  color  that  are  unfamiliar  to  them.  But  the  in- 
experienced beginner  in  geometry  will  be  no  less  sur- 
prised and  disappointed  than  the  young  musician  or 
decorator. 

The  mathematician,  the  composer,  the  decorator, 
and  the  student  of  natural  science,  when  indulging  in 
speculative  flights,  pursue  quite  analogous  modes  of  pro- 
cedure, despite  the  differences  of  their  matter  and  aim. 
The  former,  it  is  true,  owing  to  his  more  limited  ma- 
terial, has  the  advantage  of  the  others  as  regards  the 
certainty  of  his  procedure;  while  the  latter  for  the 
opposite  reason  is  at  a  disadvantage  as  compared 
with  the  others. 

19. 

In  like  manner,  the  thne  of  the  physicist  does  not 
coincide  with  the  system  of  Xime-sensations.  When  the 
physicist  wishes  to  determine  a  period  of  time,  he  ap- 
plies, as  his  instruments  of  measurement,  identical 
processes  or  processes  assumed  to  be  identical j  such  as 
vibrations  of  a  pendulum,  the  rotations  of  the  earth, 
etc.  The  fact  connected  with  the  time-sensation  is  in 
this  manner  made  the  subject  of  a  reaction,  and  the 
result  of  the  latter,  the  number  which  is  obtained, 
serves,  in  place  of  the  time-sensation,  to  determine 


i8o  THE  ANALYSIS  OF  THE  SENSATIONS. 

more  exactly  the  subsequent  movement  of  the  thought. 
In  like  manner,  we  regulate  our  thoughts  concerning 
thermal  processes  not  according  to  the  sensation  of 
warmth  which  bodies  yield  us,  but  according  to  the 
much  more  definite  sensation  which  is  obtained  from 
ihermometrical  reactions  by  simply  noting  the  height  of 
the  mercury.  Usually  a  space-sensation  (the  dial  of 
a  clock)  is  substituted  for  the  sensation  of  time,  and 
for  this,  again,  a  number  is  put.  For  example,  if  we 
represent  the  excess  of  the  temperature  of  a  cooling 
body  over  that  of  its  surroundings  by  5  :=  0^*',  then 
/  is  this  number. 

The  relation  which  the  quantities  of  an  equation 
actually  represent,  is  usually  (analytically)  a  more 
general  one  than  that  which  is  meant  to  be  repre- 
sented by  the  equation.  Thus  in  the  equation  {xjdf 
-f  (j/by  =  1  all  possible  values  of  x  have  an  analytical 
meaning,  and  yield  corresponding  values  of  y.  But  if 
the  equation  be  used  to  represent  an  ellipse,  then  only 
the  values  oi  x  <,a  and  y  <^d  have  a  geometrical  (or 
real)  significance. 

Similarly,  it  would  have  to  be  expressly  added,  if 
this  were  not  obvious,  that  the  equation  5  =  Sj-^*  re- 
presents the  real  process  only  for  increasing  values 
of/. 

If  we  imagine  the  natural  course  of  different 
events,  say  the  cooling  of  one  body  and  the  free  des- 
cent of  a  second,  represented  by  equations  involving 
time,  the  time  may  be  eliminated  from  these  equa- 


PHYSICS.  i8i 

tions,  and  we  may  express,  for  example,  the  space 
traversed  by  the  falling  body  in  terms  of  the  excess  of 
temperature.  Thus  viewed,  the  elements  appear  sim- 
ply as  dependent  on  one  another.  But  the  meaning  of 
such  an  equation  must  be  more  exactly  defined  by 
premising  that  only  increasing  distances  of  descent  or 
decreasing  temperatures  are  to  be  inserted  successively 
therein. 

Time  is  not  reversible.  A  warm  body  set  in  cool 
surroundings  simply  cools  off  but  does  not  grow  warm 
again.  With  increasing  time-sensations  only  decreas- 
ing excesses  of  temperature  are  connected.  A  house 
in  flames  burns  down  but  never  builds  itself  up 
again.  A  plant  does  not  decrease  in  size  and  creep 
into  the  earth,  but  grows  out  of  it,  increasing  in  size. 
The  irreversibility  of  time  reduces  itself  to  the  fact 
that  the  value-changes  of  physical  quantities  always 
take  place  in  definite  directions.  Of  the  two  analytical 
possibilities  one  only  is  actual.  We  do  not  need  to 
see  in  this  fact  a  metaphysical  problem. 


APPENDIX  I. 


FACTS  AND  MENTAL  SYMBOLS.^ 

T  PURSUED  in  my  youth  physical  ««^  philosoph- 
-^  ical  studies,  particularly  psychology,  with  equal 
ardor.  At  that  time  there  was  hardly  a  question  of  an 
experimental  psychology,  of  a  relation  of  psychologi- 
cal to  physiological  research.  Neither  did  the  physics 
of  that  day  think  of  a  psychological  analysis  of  the  no- 
tions it  was  constantly  employing.  How  the  notions 
of  ''body,"  ** matter,*'  ''atom,"  etc.,  originated,  was 
not  investigated.  Objects  were  given  the  inviolability 
of  which  physicists  never  questioned  and  with  which 
they  unconcernedly  pursued  their  labors. 

The  fields  of  physical  and  psychological  research 
thus  stood  side  by  side  unreconciled^  each  having  its 
own  particular  concepts,  methods,  and  theories.  No 
one  doubted  that  the  two  departments  were  in  some 

1  written  in  1891,  and  published  in  The  Monist  of  January,  1892  (Vol.  II., 
No.  a),  in  continuation  of  the  discussion  with  Dr.  Paul  Carus  in  Vol.  I.,  No.  3 
of  The  Monist  on  "  Some  Questions  of  Psycho-physics."  The  few  controver- 
sial references  are  omitted.  Professor  Mach  is  explaining  the  grounds  which 
led  him  to  abandon  his  early  position,  that  Nature  has  two  sides,  a  physical 
and  a  psychological,  which  view  he  likens  to  that  held  by  the  editor  of  The 
M^niti.— Trans. 


APPENDIX  I.  183 

way  connected.  But  the  nature  of  the  connexion  ap- 
peared an  insoluble  riddle,  as  it  still  appears  to  Dubois- 
Reymond. 

Now  although  this  condition  of  things  was  not 
such  as  to  satisfy  my  mind,  it  was  nevertheless  nat- 
ural that  as  a  student  I  should  seek  to  acquire  tenta- 
tively the  dominant  views  of  the  two  provinces  and  to 
put  them  into  consistent  connexion  with  one  another. 

I  thus  formed  provisorily  the  view  that  Nature  has 
two  sides — a  physical  and  a  psychological  side.  If 
psychical  life  is  to  be  harmonised  at  all  with  the  the- 
ories of  physics,  we  are  obliged,  I  reasoned,  to  con- 
ceive of  atoms  as  feeling  (ensouled).  The  various 
dynamic  phenomena  of  the  atoms  would  then  repre- 
sent the  physical  processes,  whilst  the  internal  states 
connected  therewith  would  be  the  phenomena  of  psychic 
life.  If  we  accept  in  faith  and  seriousness  the  atom- 
istic speculations  of  the  physicists  and  of  the  early 
psychologists  (on  the  unity  of  the  soul),  I  still  see 
no  other  way  of  arriving  at  a  tenable  monistic  con- 
ception. 

It  is  unnecessary  to  emphasise  at  length  here  the 
prominent  part  which  the  artificial  scaffolding  em- 
ployed in  the  construction  of  knowledge  plays  in 
these  monadic  theories  as  contradistinguished  from 
the  facts  which  really  deserve  to  be  known,  and  the 
scant  satisfaction  which  such  theories  afford  in  the 
long  run.  As  a  fact,  employment  with  this  cumbrous 
artifice  was  in  my  case  the  very  means  that  gave  rise 


i84  THE  ANALYSIS  OF  THE  SENSATIONS. 

to  my  better  conviction,  which  was  already  latently 
present.^ 

In  the  further  progress  of  my  physical  work  I  soon 
discovered  that  it  was  very  necessary  sharply  to  dis- 
tinguish between  what  we  see  and  what  we  mentally 
supply.  When,  for  example,  I  imagine  heat  as  a  sub- 
stance (a  fluid)  that  passes  from  one  body  to  another, 
I  follow  with  ease  the  phenomena  of  conduction  and 

lA  Greek  philosopher  to  whom  change  of  spatial  configuration,  pressure, 
and  impact  were  probably  the  only  natural  processes  with  which  he  was  in- 
timately acquainted,  thought  out  the  atomistic  theory.  This  theory  we  retain 
to-day,  though  in  a  modified  form.  And  in  fact  natural  phenomena  really  do 
exist  such  that,  to  all  appearances,  the  pressure  and  impact  of  very  small 
particles  are  concerned  in  their  production  (the  dynamical  theory  of  gases), 
phenomena  that  therefore  admit  of  being  more  clearly  viewed  by  this  con- 
ception. However,  this  conception,  like  that  of  caloric,  possesses  value  only 
in  certain  fields.  We  know  to-day  that  pressure  and  impact  are  by  no  means 
simpler  phenomena  than  are  for  example  the  phenomena  of  gravitation.  The 
contention  that  in  physics  everything  can  be  reduced  to  the  motion  of  small- 
est particles  is,  at  best,  but  an  improper  draft  on  the  future.  Utterances  of 
this  kind  afford  no  assistance  in  the  solution  of  burning  special  questions, 
but  only  confound,  and  have  about  the  same  explanatory  value  as  the  utter- 
ances of  the  late  physical  philosophy  of  Oken, — a  philosophy  which,  for  ex- 
ample, reproduces  with  the  greatest  ease  the  method  of  the  creation  of  the 
world  by  a  division  of  zero-quantities  into  +a  and  — a  (o=  -fa  —  a). 

The  motion  of  a  single  body  as  a  totality  does  indeed  appear  simpler  at 
first  glance  than  any  other  process,  and  this  is  the  justification  of  attempts  at 
a /A^*/Va/ monadic  theory.  The  thoughts  of  a  single  man  are  connected  to- 
gether; the  thoughts  of  two  different  men  are  not.  How  can  the  processes  of 
the  different  parts  of  the  brain  of  one  man  be  connected  ?  In  order  to  make 
the  connexion  very  intimate,  we  conceive  everything  that  requires  to  be  psy- 
chically connected,  as  collected  in  a  single  point,  although  the  connexion  is 
not  explained  by  our  procedure.  Thus  the  psychological  monadic  theory 
rests  on  a  motive  and  on  an  illusion  quite  similar  to  those  on  which  the  phys- 
ical rests. 

Let  us  assume  for  a  moment  the  proposition  in  the  text;  viz.,  that  the 
atoms  are  endowed  with  feeling.  By  the  space-co6rdinates  x,y,  z,  x',y\  z'. . .  of 
the  atoms  are  determined  in  the  atoms  internal  conditions  a,  jS,  y,  a',  /?',  y'..., 
and  vice  versa.  For  we  feel  by  our  senses  our  physical  environment,  and  our 
reactions  upon  our  environment  are  conditioned  by  our  sensations.  The  idea 
then  suggests  itself,  since  a  3y  .  .  .  alone  are  directly  given,  to  set  up  by  the 
elimination  of  jc,y,z...  equations  directly  between  a/?y,  a' P' y' .  .  .  . 
This  view  would  very  nearly  approach  to  my  present  one,  (apart  from  the  fact 
that  the  latter  entirely  rejects  metaphysical  considerations). 


APPENDIX  I,  Z85 

exchange.  This  idea  led  Black,  who  established  it, 
to  the  discovery  of  specific  heat,  of  the  latent  heat  of 
fusion  and  vaporisation,  and  so  forth.  This  same  idea 
of  a  constant  quantity  of  heat-substance,  on  the  other 
hand,  prevented  Black's  successors  from  using  their 
eyes.  They  no  longer  observe  the  fact  which  every 
savage  knows,  that  heat  is  produced  by  friction.  By 
the  help  of  his  undulatory  theory  Huygens  follows 
with  ease  the  phenomena  of  luminous  reflexion  and 
refraction.  The  same  theory  prevents  him  (for  he 
thinks  solely  of  the  longitudinal  waves  with  which  he 
is  familiar),  from  rightly  grasping  the  fact  of  polarisa- 
tion which  he  himself  discovered,  but  which  Newton, 
on  the  other  hand,  untrammelled  by  theories,  perceives 
at  once.  The  conception  of  fluids  acting  at  a  distance 
on  conductors  charged  with  electricity  facilitates  our 
view  of  the  behavior  of  the  objects  charged,  but  it 
stood  in  the  way  <7/"the  discovery  of  the  specific  induc- 
tive capacity,  which  was  reserved  for  the  eye  of  Fara- 
day undimmed  by  traditional  conceptions. 

Valuable,  therefore,  as  are  the  conceptions  which 
we  mentally  (theoretically)  supply  in  investigating 
facts,  bringing  to  bear,  as  they  do,  older,  richer,  more 
general,  and  more  familiar  experiences  on  facts  that 
stand  alone,  thus  affording  us  a  broader  field  of  view, 
nevertheless,  the  same  conceptions  may  lead  us  astray 
as  classical  examples  and  our  own  experience  demon- 
strate. For  a  theory,  indeed,  always  puts  in  the  place 
of  a  fact  something  different,  something  more  simple, 


x86  THE  ANALYSIS  OF  THE  SENSA7U0NS. 

which  is  qualified  to  represent  the  fact  in  some  certain 
aspect,  but  for  the  very  reason  that  it  is  different  does 
not  represent  it  in  other  aspects.  When  in  the  place 
of  light  Huygens  mentally  put  the  familiar  phenom- 
enon of  sound,  light  itself  appeared  to  him  as  a  thing 
that  he  knew,  but  with  respect  to  polarisation,  which 
sound-waves  lack,  as  a  thing  with  which  he  was  doubly 
unacquainted.  Our  theories  are  abstractions,  which, 
while  placing  in  relief  what  is  important  in  certain 
determinate  cases,  neglect  almost  necessarily,  or  even 
disguise,  what  is  important  in  other  cases.  The  law 
of  refraction  looks  upon  rays  of  light  as  homogeneous 
straight  lines,  and  that  is  sufficient  for  the  comprehen- 
sion of  the  geometrical  aspect  of  the  matter.  But  the 
propositions  relating  to  refraction  will  never  lead  us 
to  the  fact  that  the  rays  of  light  are  periodical,  that 
they  interfere.  On  the  contrary,  the  favorite  and 
familiar  conception  of  a  ray  as  an  undifferentiated 
straight  line  is  more  likely  to  render  this  discovery 
difficult. 

The  instances  in  which  the  resemblance  between  a 
fact  and  its  theoretical  conception  extends  further  than 
we  ourselves  postulate,  are  rare.  But  when  this  hap- 
pens, the  theoretical  conception  may  lead  to  the  dis- 
covery of  new  facts,  a  case  of  which  conical  refraction, 
circular  polarisation,  and  Hertz's  electric  waves  furnish 
examples  that  militate  against  those  above  advanced. 
As  a  general  rule,  however,  there  is  every  reason  for 
distinguishing  sharply  between  our  theoretical   con- 


APPENDIX  /.  187 

ceptlons  of  phenomena  and  that  which  we  observe. 
The  former  must  be  regarded  merely  as  auxiliary  in- 
struments which  have  been  created  for  a  definite  pur- 
pose and  which  possess  permanent  value  only  with 
respect  to  that  purpose.  No  serious  person  will  im- 
agine for  a  moment  that  real  circles  with  angles  and 
sines  perform  functions  in  the  refraction  of  light. 
Every  one,  on  the  contrary,  regards  the  formula 
sina/siny^  = «  as  a  kind  of  geometrical  model  which 
simply  imitates  inform  the  refraction  of  light  and  takes 
its  place  in  our  mind.  Now,  in  this  sense,  I  take  it, 
all  theoretical  conceptions  of  physics — caloric,  elec- 
tricity, light-waves,  molecules,  atoms,  and  energy — 
must  be  regarded  as  mere  helps  or  expedients  to  facil- 
itate our  consideration  of  things.  Even  within  the 
domain  of  physics  itself  the  greatest  care  must  be  ex- 
ercised in  transferring  theories  from  one  department 
to  another,  and  above  all  more  information  is  not  to 
be  expected  from  a  theory  than  from  the  facts  them- 
selves. 

On  the  other  hand,  there  is  no  lack  of  instances 
showing  the  far  greater  confusion  which  was  produced 
by  the  direct  transference  of  theories,  methods,  and 
inquiries  that  were  legitimate  in  physics,  into  the  field 
of  psychology. 

Allow  me  to  illustrate  this  by  a  few  examples. 

A  physicist  observes  an  image  on  the  retina  of  an 
excised  eye,  notices  that  it  is  turned  upside  down  with 
respect  to  the  objects  imaged,  and  puts  to  himself 


z88  THE  ANALYSIS  OF  THE  SENSATIONS. 

very  naturally  the  question,  How  does  a  luminous 
point  situated  at  the  top  come  to  be  reflected  on  the 
retina  at  the  bottom  ?  He  answers  this  question  by  the 
aid  of  studies  in  dioptrics.  If,  now,  this  question, 
which  is  perfectly  legitimate  in  the  province  of  phys- 
ics, be  transferred  to  the  domain  of  psychology,  only 
obscurity  will  be  produced.  The  question  why  we  see 
the  inverted  retinal  image  upright^  has  no  meaning  as 
a  psychological  problem.  The  light-sensations  of  the 
separate  spots  of  the  retina  are  connected  with  sensa- 
tions of  locality  from  the  very  outset,  and  we  name  the 
places  that  correspond  to  the  parts  down,  up.  To  the 
perceiving  subject  such  a  question  cannot  present  it- 
self. 

It  is  the  same  with  the  well-known  theory  of  pro- 
jection. The  problem  of  the  physicist  is,  to  seek  the 
luminous  object-point  of  a  point  imaged  on  the  retina 
of  the  eye,  in  the  backward  prolonged  ray  passing 
through  the  centre  of  the  eye.  For  the  perceiving 
subject  this  problem  does  not  exist,  as  the  light-sensa- 
tions of  the  retinal  spots  are  connected  from  the  be- 
ginning with  determinate  space-sensations.  The  en- 
tire theory  of  the  psychological  origin  of  the  '^external " 
world  by  the  projection  of  sensations  outwards  is 
founded  in  my  opinion  on  a  mistaken  transference  of 
a  physically  formulated  inquiry  into  the  province  of 
psychology.  Our  sensations  of  sight  and  touch  are 
bound  up  with,  are  connected  with,  various  different 
sensations  of  space,  that  is  to  say,  the  sensations  in 


APPENDIX  I.  189 

question  have  an  existence  by  the  side  of  one  another 
or  outside  of  one  another,  exist,  in  other  words,  in  a 
spatial  field,  in  which  our  body  fills  but  a  part.  That 
table  is  thus  self-evidently  outside  of  my  body.  A  pro- 
jection-problem does  not  present  itself,  is  neither  con- 
sciously nor  unconsciously  solved. 

A  physicist  (Mariotte)  discovers  that  a  certain  spot 
on  the  retina  is  blind.  He  is  accustomed  to  associat- 
ing with  every  spatial  point  an  imaged  point,  and  with 
every  imaged  point  a  sensation.  Hence  the  question 
arises,  What  do  we  see  at  the  points  corresponding  to 
the  blind  spots,  and  how  is  the  gap  in  the  image  filled 
out  ?  If  the  unfounded  influence  of  the  physicist's 
methods  on  the  discussion  of  psychological  questions 
be  excluded,  it  will  be  found  that  no  problem  exists  at 
all  here.  We  see  nothing  at  the  blind  spots,  the  gap  in 
the  image  is  not  filled  out.  The  gap,  furthermore,  is 
not  felt,  for  the  reason  that  a  defect  of  light-sensation 
at  a  spot  blind  from  the  beginning  can  no  more  be  per- 
ceived as  a  gap  in  the  image  than  the  blindness  say  of 
the  skin  of  the  back  can  be  so  perceived. 

I  have  intentionally  chosen  simple  and  obvious  ex- 
amples, as  they  can  best  render  clear  what  unneces- 
sary confusion  is  caused  by  the  careless  transference 
of  a  conception  or  mode  of  thought  which  is  valid  and 
serviceable  in  one  domain,  into  another. 

In  the  work  of  a  celebrated  German  ethnographer 
I  recently  read  the  following  sentence:  ''This  tribe 
of  people  deeply  degraded  itself  by  the  practice  of 


igo  THE  ANALYSIS  OF  THE  SENSATIONS. 

cannibalism."  By  its  side  lay  the  book  of  an  Eng- 
lish inquirer  who  deals  with  the  same  subject.  The 
latter  simply  puts  the  question  why  certain  South-Sea 
Islanders  eat  human  beings,  finds  out  in  the  course  of 
his  inquiries  that  our  own  ancestors  were  once  canni- 
bals, and  comes  to  understand  the  position  the  Hindus 
take  in  the  matter  -a  point  of  view  that  occurred  once 
to  my  five  year-old  boy  who  while  eating  a  piece  of 
meat  stopped,  suddenly  shocked,  and  cried  out,  ^'We 
are  cannibals  to  the  animals  !  "  **  Thou  shalt  not  eat 
human  beings  "  is  a  very  beautiful  maxim  ;  but  in  the 
mouth  of  the  ethnographer  it  sullies  the  calm  and 
noble  lustre  of  unprepossession  by  which  we  so  gladly 
discover  the  true  inquirer.  But  a  step  further  and  we 
shall  say,  *'Man  must  not  be  descended  from  mon- 
keys," **The  earth  shall  not  rotate,"  *' Matter  ^«^/r/ 
not  everywhere  to  fill  space,"  **  Energy  wwj-/  be  con- 
stant," and  so  on.  I  believe  that  our  procedure  differs 
from  that  just  characterised  only  in  degree  and  not  in 
kind,  when  we  transfer  views  reached  in  the  province 
of  physics,  with  the  dictum  of  sovereign  validity,  into 
the  domain  of  psychology,  where  they  should  be  tested 
anew  with  respect  to  their  serviceability.  In  such 
cases  we  are  subject  to  dogma,  if  not  to  dogma  which 
is  forced  upon  us  by  a  power  from  without  like  our 
scholastic  forefathers,  yet  to  that  which  we  have  cre- 
ated ourselves.  And  what  result  of  research  is  there 
that  could  not  become  a  dogma  by  long  habit  and  use, 
since  the  very  skill  which  we  have  acquired  in  familiar 


APPENDIX  I.  191 

intellectual  situations  deprives  us  of  the  freshness  and 
unprepossession  which  are  so  requisite  in  the  new ! 

Now  that  I  have  set  forth  in  general  outlines  the 
position  I  take,  I  may  perhaps  be  able  to  explain  my 
opposition  to  the  dualism  of  feeling  and  motion.  This 
dualism  is  to  my  mind  artificial  and  unnecessary.  Its 
origin  is  analogous  to  that  of  certain  pseudo-mathe- 
matical problems, — having  come  from  an  improper 
formulation  of  the  questions  involved. 

In  the  investigation  of  purely  physical  processes 
we  generally  employ  concepts  of  so  abstract  a  char- 
acter that  as  a  rule  we  think  only  cursorily,  or  not  at 
all,  of  the  sensations  that  lie  at  their  base.  For  ex- 
ample, when  I  ascertain  the  fact  that  an  electric  cur- 
rent having  the  strength  of  i  Ampere  develops  10 J 
cubic  centimetres  of  oxyhydrogen  gas  at  o®  C.  and  760 
mm  mercury-pressure  in  a  minute,  I  am  readily  dis- 
posed to  attribute  to  the  objects  defined  a  reality 
wholly  independent  of  my  sensations.  But  I  am 
obliged,  in  order  to  arrive  at  what  I  have  determined, 
to  conduct  the  current  through  a  circular  wire  having 
a  definite  measured  radius,  so  that  the  current,  the 
intensity  of  terrestrial  magnetism  being  given,  shall 
turn  the  magnetic  needle  at  its  centre  a  certain  angu- 
lar distance  out  of  the  meridian.  The  intensity  of 
terrestrial  magnetism  must  have  been  disclosed  by  a 
definite  observed  period  of  vibration  of  a  magnetic 
needle  of  measured  dimensions,  known  weight,  and 
so  forth.     The  determination  of  the  oxyhydrogen  gas 


Z92  THE  ANALYSIS  OF  THE  SENSATIONS. 

IS  no  less  intricate.  The  whole  statement,  so  simple 
in  its  appearance,  is  based  upon  an  almost  unending 
series  of  simple  sensory  observations  (sensations),  par- 
ticularly if  we  take  into  consideration  the  observations 
that  assure  the  adjustment  of  the  apparatus,  which 
may  have  been  performed  in  part  long  before  the  ac- 
tual experiment.  Now  it  can  easily  happen  to  the 
physicist  who  does  not  study  the  psychology  of  his 
operations,  that  he  does  not  (to  reverse  a  well-known 
saying)  see  the  trees  for  the  woods,  that  he  slurs  over 
the  sensory  elements  at  the  foundation  of  his  work. 
Now  I  maintain  that  every  physical  concept  is  nothing 
but  a  certain  definite  connexion  of  the  sensory  elements 
which  1  denote  hy  A  B  C .  .  .,  and  that  every  physical 
fact  rests  therefore  on  such  a  connexion.  These  ele- 
ments— elements  in  the  sense  that  no  further  resolu- 
tion has  as  yet  been  made  of  them — are  the  simplest 
building -stones  of  the  physical  world  that  we  have  yet 
been  able  to  reach. 

Physiological  research  also  may  be  of  a  purely 
physical  character.  I  can  follow  the  course  of  a  phys- 
ical process  as  it  propagates  itself  through  a  sensitive 
nerve  to  the  spinal  cord  and  brain  of  an  animal  and  re- 
turns by  various  paths  to  the  muscles,  whose  contrac- 
tion produces  further  effects  in  the  environment  of 
the  animal.  I  need  not  think,  in  so  doing,  of  any  feel- 
ing on  the  part  of  the  animal ;  what  I  investigate  is  a 
purely  physical  object.  Very  much  is  lacking,  it  is 
true,  to  our  complete  comprehension  of  the  details  of 


APPENDIX  I, 


193 


this  process,  and  the  assurance  that  it  is  all  motion 
can  neither  console  me  nor  deceive  me  with  respect 
to  my  ignorance. 

Long  prior  to  scientific  psychology  people  had 
perceived  that  the  behavior  of  an  animal  confronted 
by  physical  influences  is  much  better  grasped,  that  is 
understood,  by  attributing  to  the  animal  sensations  like 
our  own.  To  that  which  I  see,  to  my  sensations,  I 
have  to  supply  mentally  the  sensations  of  the  animal, 
which  are  not  to  be  found  in  the  province  of  my  own 
sensation.  This  opposition  appears  even  more  abrupt 
to  the  scientific  inquirer  who  is  investigating  a  nervous 
process  by  the  aid  of  colorless  abstract  concepts,  and 
is  required  for  example  to  add  mentally  to  that  process 
the  sensation  green.  This  last  may  actually  appear 
as  something  entirely  novel,  and  we  may  ask  ourselves 
how  it  is  that  this  miraculous  thing  is  produced  from 
chemical  processes,  electrical  currents,  and  the  like.^ 

Psychological  analysis  has  taught  us  that  this  sur- 
prise is  unjustifiable,  since  the  physicist  deals  with 

IThe  following  is  a  legitimate  question:  To  what  kind  of  nervous  pro- 
cesses is  the  sensation  green  to  be  mentally  added?  Such  questions  can  be 
solved  only  by  special  inquiry,  and  not  by  reference  in  a  general  way  to  motion 
and  electric  currents.  How  disadvantageous  it  is  for  us  to  remain  satisfied 
with  such  general  conceptions  can  be  seen  from  the  fact  that  inquirers 
have  been  repeatedly  on  the  brink  of  abandoning  the  specific  energies,  one  of 
the  greatest  acquisitions  we  have  made,  simply  because  they  were  unable  to 
discover  any  difference  in  the  currents  of  different  sensory  nerves.  I  was 
impelled  as  early  as  1863  in  my  lectures  on  psycho-physics  to  call  attention  to 
the  fact  that  the  most  diverse  kinds  of  nervous  processes  can  conceal  them- 
selves in  a  current.  Current  is  an  abstraction  and  places  in  relief  but  one 
feature  of  the  process— the  passage  of  energy  through  a  transverse  section.  A 
current  in  diluted  sulphuric  acid  is  something  entirely  different  from  a  cur- 
rent in  copper.  We  must  therefore  expect  also  that  a  current  in  the  acoustic 
nerve  will  be  something  entirely  different  from  a  current  in  the  optic  nerve. 


194  I^HE  ANALYSIS  OF  THE  SENSATIONS. 

sensations  in  all  his  work.  The  same  analysis  may 
also  show  us  that  the  mental  addition  by  analogy  of 
sensations  and  complexes  of  sensations  which  at  the 
time  being  are  not  present  in  the  field  of  sense  or 
cannot  even  come  into  it,  is  daily  practised  by  the 
physicist,  as,  for  example,  when  he  imagines  the  moon 
an  inert  heavy  mass,  although  he  cannot  touch  the 
moon  but  can  only  see  it.  The  totally  strange  charac- 
ter of  the  intellectual  situation  above  described  is 
therefore  an  illusion. 

The  illusion  disappears  when  I  make  observations 
(psychologically)  on  my  own  person,  which  are  lim- 
ited to  the  sensory  sphere.  Before  me  lies  the  leaf  of 
a  plant.  The  green  {A)  of  the  leaf  is  united  with  a 
certain  optical  sensation  of  space  {B)  and  sensation  of 
touch  (C),  and  with  the  visibility  of  the  sun  or  the 
lamp  (Z>).  If  the  yellow  (^)  of  a  sodium  flame  takes 
the  place  of  the  sun,  the  green  (^)  will  pass  into 
brown  {Fy  If  the  chlorophyl  granules  be  removed, — 
an  operation  representable,  like  the  preceding  one,  by 
elements, — the  green  (^)  will  pass  into  white  ((9). 
All  these  observations  are  physical  observations.  But 
the  green  {A  )  is  also  united  with  a  certain  process  on 
my  retina.  There  is  nothing  to  prevent  me  in  prin- 
ciple from  physically  investigating  this  process  in  my 
own  eye  in  exactly  the  same  manner  as  in  the  cases 
previously  set  forth,  and  from  reducing  it  to  its  ele- 
ments X  Y  Z.  ,  ,  .  \i  this  were  not  possible  in  the  case 
of  my  own  eye,  it  might  be  accomplished  with  that 


APPENDIX  I.  195 

of  another,  and  the  gap  filled  out  by  analogy,  exactly 
as  in  physical  investigations.  Now  in  its  dependence 
upon  B  C D.  .  .  ,j  A  is  a  physical  element,  in  its  de- 
pendence on  X  yZ .  .  .  it  is  a  sensation.  The  green 
{A ),  however,  is  not  altered  at  all  in  itself ,  whether 
we  direct  our  attention  to  the  one  or  to  the  other  form 
of  dependence,  /  see,  therefore,  no  opposition  of  physi- 
cal and  psychical,  no  duality,  but  simply  identity.  In  the 
sensory  sphere  of  my  consciousness  everything  is  at 
once  physical  and  psychical. 

The  obscurity  of  this  intellectual  situation  has,  I 
take  it,  arisen  solely  from  the  transference  of  a  phys- 
ical prepossession  to  the  domain  of  psychology.  The 
physicist  says :  I  find  everywhere  bodies  and  the  mo- 
tions of  bodies  only,  no  sensations  ;  sensations,  there- 
fore, must  be  something  entirely  different  from  the 
physical  objects  I  deal  with.  The  psychologist  accepts 
the  second  portion  of  this  declaration.  To  him,  it  is 
true,  sensation  is  given,  but  there  corresponds  to  it  a 
mysterious  physical  something  which  conformably  to 
physical  prepossession  must  be  different  from  sensa- 
tion. But  what  is  it  that  is  the  really  mysterious 
thing  ?  Is  it  the  Physis  or  the  Psyche  ?  Or  is  it  per- 
haps both  ?  It  would  almost  appear  so,  as  it  is  now 
the  one  and  now  the  other  that  is  intangible.  Or  does 
the  whole  argument  rest  on  a  vicious  circle  ? 

I  believe  that  the  latter  is  the  case.  For  me  the 
elements  designated  by  ^  ^  C  .  .  are  immediately 
and  indubitably  given,  and  for  me  they  can  never 


196  THE  ANALYSIS  OF  THE  SENSATIONS. 

afterwards  be  volatilised  away  by  considerations  which 

ultimately  are  always  based  on  their  existence.^ 

For  that  department  of  special  research  having  for 

its  subject  the  sensory,  physical,  and  psychical  prov- 

rhce  which  is  not  made  superfluous  by  this  general 

orientation  and  which  cannot  be  forestalled,  only  the 

relations  oi  A  B  C  .  .  .  remain  to  be  ascertained.  This 

may  be  expressed  symbolically  by  saying  that  it  is  the 

purpose  and  end  of  special  research  to  find  equations 

of  the  form  f  {A,  By  C .  .  .)=o. 

* 

This  whole  train  of  reasoning  has  for  me  simply 
the  significance  of  negative  orientation  for  the  avoid- 
ance of  pseudo-problems.  Moreover,  I  intentionally 
restrict  myself  here  to  the  question  of  sense-percep- 
tions, for  the  reason  that  at  the  start  exact  special  re- 
search will  find  here  alone  a  safe  basis  of  operations. 

1  It  is  the  transitoriness  of  sense-perceptions  that  so  easily  leads  us  to 
regard  them  as  mere  appearances  in  contrast  with  permanent  bodies.  I  have 
repeatedly  pointed  out  that  unconditioned  permanent  things  do  not  exist  in 
nature,  that  permanences  of  connexion  only  exist.  A  body  is  for  me  the  same 
complex  of  sight-and-touch-sensations  every  time  that  it  is  placed  in  the  same 
circumstances  of  illumination,  position  in  space,  temperature,  and  so  forth. 
The  supposed  constancy  of  the  body  is  the  constancy  of  the  union  of  yj  B 
C. . .  or  the  constancy  of  the  equation  /  {^,  B,  C . . .}  =  o. 


APPENDIX  II, 


A  NEW  ACOUSTIC  EXPERIMENT  BY  E.  MACH.l 

TN  A  box  having  double  walls,  the  intervening  space 
-■-  of  which  is  packed  with  sawdust,  is  placed  an 
electric  tuning-fork,  reed-pipe,  or  other  musical  in- 
strument which  can  be  easily  excited  from  without. 
(See  next  page,  Fig.  37,  which  is  drawn  from  memory.) 
From  this  box  runs  a  tube  which  divides  into  two 
branches.  One  of  these  branches  leads  to  a  KOnig's 
manometric  capsule ;  the  other  is  carried  close  to  a 
pasteboard  disc  where  it  breaks  but  on  the  other  side 
is  continued  again  to  the  ear  of  the  observer.  The 
pasteboard  disc,  which  can  be  turned  like  the  disc  of 
an  electrical  machine,  has  a  radial  slit  of  variable 
angular  width,  and  carries  at  the  proper  inclination  to 
its  axis  a  mirror  into  which  the  observer  can  look 
through  the  slit. 

Exciting  the  apparatus  in  the  box,  and  putting  the 
eye  close  to  the  disc,  which  is  now  set  in  rotation,  the 
ear  receives  the  impression  of  a  uniform  tone,  the 

I  Extract  from  Loios,  Prague,  August,  1873.     Reprinted  to  elucidate  the 
reference  on  page  124. 


198 


THE  ANALYSIS  OF  THE  SENSATIONS. 


duration  of  which  is  curtailed  by  the  slit.  In  the  ro- 
tating mirror  is  seen  the  image  of  the  manometric 
gas-jet,  which  is  resolved  into  distinct  and  single 
flames,  the  resultant  action  of  the  slit  being  that  the 


Fig.  37. 

(Diagram Explaining  "A  New  Acoustic  Experiment  by  E.  Mach." 
Drawn  from  memory.) 
T,  electric  tuning-fork.    BB,  box  with  double  walls.    R,  resonator,    ttt, 
tube.    M,  Manometric  capsule.     22,  rotating  disc  with  variable  slit  WW. 
oa,  mirror  attached  to  the  disc  behind  the  slit.    E,  the  ear.     O,  the  eye. 


observer  sees  as  many  vibrations  as  he  hears.  We  can 
count  thus,  by  enumerating  the  images  of  the  flames, 
the  number  of  vibrations  reaching  the  ear,  and  so  con- 
vince ourselves  that  for  the  production  of  the  sensa- 


APPENDIX  II,  199 

tion  of  tone  a  certain  number  of  vibrations  are  required. 
If  the  ear  receives  too  few  vibrations  no  tone  is  no- 
ticed, but  only  a  short,  sharp  concussion,  in  which  no 
pitch  is  distinguishable.  A  low  tone  of  one  hundred 
and  twenty-eight  full  vibrations  is  recognisable  as  a 
tone  of  definite  pitch  only  upon  four  to  five  vibrations 
striking  the  ear  ;  with  two  or  three  vibrations  it  pro- 
duces only  a  sharp  concussion.  In  the  case  of  low 
tones  the  harmonics  are  distinctly  heard  when  the  fun- 
damental, from  its  brief  duration,  is  undistinguish- 
able. 


ADDENDA. 


Paob  97,  LAST  FOOTNOTE. — Add  the  words :  "The  same  phe- 
Bomena  may  also  be  observed  in  connexion  with  tke  shadow  of 
the  moon  and  of  the  planets  (Seeliger,  Abhattdlungtn  tUr  MUn- 
chener  Akademit,  II.  CI.,  XIX.  Bd.,  II.  Abtheil.,  1896).- 

Paox  105. — Add  as  a  footnote  to  the  last  line  of  paragraph  ix : 
"Compare  on  this  point  Jacques  Loeb,  Uth^r  dtn  Nachwsis  von 
ContrasterschHnungen  im  Gebiete  der  Raunumpjindungtn  dts  Augei, 
Archivf.  Fhysiologie,  Bd.  60,  1895," 


INDEX. 


.^  5  C.  ...  the  complexes.  See  Ele- 
ments, apy  .  .  .  ,  the  complexes. 
See  Elements. 

Absent-mindedness,  85. 

Abstraction,  160  at  seq.,  165. 

Accelerations,  organ  reacting  upon, 
74  et  seq. 

Acoustic  color,  138. 

Acute  angles,  vision  of,  103-105. 

Adaptation,  organic,  40,  83 ;  mental, 
24,  156,  159. 

iEsthetics,  repetition  in,  53-56 ;  asso- 
ciation in,  121. 

Afi&nity,  geometrical,  55. 

After-images,  61,  113,  178. 

Allen,  Grant,  42  footnote. 

Ampfere's  swimmer,  173. 

Anachronisms  in  dreams,  114. 

Analysis,  5. 

Angles,  underestimation  and  over- 
estimation  of,  103. 

Animals,  their  psychical  powers,  82- 
83. 

Antithesis  of  world  and  ego,  11. 

Apparatus  for  observing  animals  in 
rotation,  74  footnote  et  seq. 

Association,  in  aesthetics,  i2i. 

Atomic  theories,  25,  184  footnote. 

Atoms,  152-154,  167;  ensouled,  183. 

Attention,  work  of,  felt  as  time,  iii 
et  seq;  time  required  for  its  trans- 
ference, 113;  fixing  and  wandering 
of.  132  et  seq.;  165. 

Attributes,  6. 

Aubert,  34  footnote. 

Auditive  organ,  theory  of,  123,  128  et 
seq.,  142  et  seq.,  147. 

Auerbach,  125  footnote. 


Automata,  83  footnote. 
Auxiliary  conceptions,  155-156. 
Avenarius,  23  footnote,  26  footnote. 

Beats,  in  harmony,  120,  123,  138. 

Beetles,  82  footnote. 

Benndorf,  42  footnote. 

Berg,  H.,  120. 

Berkeley,  65  footnote. 

Bernoulli,  John,  56. 

Black,  185. 

Blind,  space-sense  of,  65  footnote. 

Blind  spot  of  the  eye,  189. 

Bodies,  complexes  of  sensations,  2  et 

seq.,  22,  166  et  seq.,  196  footnote.; 

relation  of  the  ego  to,  8-9 ;  observed 

as  wholes,  41,  93. 
Body,  the  human,  its  relation  to  the 

world,  12  et  seq. ;  152. 
Breuer,  62,  66,  67,  73,  78. 
Brewster,  32,  33. 
Bridge  and  flowing  water,  example 

of,  68. 
Brown,  Prof.  Crum,  73  footnote. 
Briicke,  125  footnote. 
Busts,  52. 

Caloric,  185. 

Cannibalism,  190. 

Cams,  Dr.  Paul,  20  footnote,  26  foot- 
note, 182  footnote. 

Causality,  need  of,  172;  and  will,  173 
footnote. 

Centric  symmetry,  46,  54-55- 

Characteristic  sensation  of  intervals, 
139  et  seq. 

Chemical  processes  and  sensation, 
43* 


THE  ANALYSIS  OF  THE  SENSATIONS. 


Children  their  sense  for  perspective, 

io6. 

Chinese,  the,  91. 

Chords,  decomposition  of,  133  et  seq. 

Circle,  97. 

Circulation,  cerebral,  Ii6. 

Clangs,  12a,  134,  147. 

Collineation,  55. 

Color  sensations,  31-35,  42-44;  com- 
pared with  tone  sensations,  130. 

Color- sense  of  the  ancients  and  mod- 
erns, 42  footnote. 

Completing,  of  facts  by  analogy,  15; 
of  incomplete  facts,  171  et  seq.,  176. 

Complexes  of  sensations,  2  et  seq.,  8 
et  seq.,  22. 

Composer,  musical,  178,  179. 

Composite  musical  sounds,  122,  i34i 
147. 

Composite  sensations,  34  footnote. 

Comprehension,  dependent  on  ac- 
tion, 164. 

Concepts,  as  labor-saving  instru- 
ments, 151  footnote;  general,  de- 
fined, 160  et  seq.;  physical,  defined, 
192. 

Conflict  of  points  of  view,  7. 

Congruence,  geometrical  and  physio- 
logical, 45  et  seq.,  177. 

Conic  sections,  163. 

Conical  polarisation,  186;  refraction, 
x86. 

Connexion,  of  the  elements,  the  sub- 
ject-matter of  science,  11;  con- 
stancies of,  the  only  constancies, 
169  et  seq.;  permanences  of,  the 
only  existences,  196  footnote. 

Consciousness,  organ  of,  112, 115-116. 

Constancies,  as  surviving  change, 
174;  of  environment  and  thought, 
166-171. 

Consumption,  organic,  of  conscious- 
ness, gives  rise  to  tense  of  time, 
III  et  seq. 

Continuity,  principle  of,  27,  158  et 
seq.;  166. 

Contrast  in  tones,  138  et  seq. 

Cornelius,  P.,  136. 

Corti,  organ  of,  123,  128  et  seq.  142  et 
seq.,  147. 

Counting,  116. 


Courtship,  music  in,  120-121. 
Current,  defined,  193  footnote. 

D'Alembert,  126. 

Darwin,  36  footnote,  38  footnote,  39, 
40,  43  footnote,  97  footnote,  120. 

Deaf  mutes,  73  footnote. 

Death,  4  footnote,  36  footnote. 

Decomposition  of  chords,  133  et  seq. 

Decorative  arts,  54,  93,  149. 

Decorator,  178,  179. 

Departure  from  the  mean  of  sensa- 
tions, 96  et  seq.,  loi. 

Depth-sensation,  52,  99  et  seq. 

Descent  of  bodies,  175  footnote. 

Determinateness,  principle  of  suflS- 
cient,  28. 

Diderot,  65  footnote. 

Differential  coefiBcients,  49. 

Differentiation,  principle  of  suffi- 
cient, 28.  158-151;,  166. 

Direction,  physiological  significance 
of,  49,  64. 

Dissonance,  126,  138. 

Dogma,  nature  of,  190. 

Double  hearing,  143. 

Dreams,  88  footnote,  114  text,  114-115 
footnote. 

Dualism  of  feeling  and  motion,  191 
et  seq. 

Duality,  principle  of,  126. 

Dubois-Reymond,  183. 

Dvorak,  112;  113  footnote,  125  foot- 
note. 

Ear,  its  function  in  orientation,  73 
footnote.  See  Auditive  Organ  and 
ToHc-Sensations. 

Earthquake,  example  of,  154. 

Economy,  of  science,  25;  principle 
of,  in  sight-sensation,  96,  100;  men- 
tal, 166. 

Ego,  its  unstable  character,  3-4  foot- 
note :  its  relation  to  bodies  and  the 
world  of  sense,  8  et  seq.,  11  et  seq.. 
14  footnote,  23  footnote;  its  origin, 
character,  and  import,  18-22;  its 
power  to  expand  and  contract,  10- 
II  text  and  footnote. 

Egyptians,  art  of,  4a  footnote,  106. 

Electric  current,  43-44. 


IMDEX, 


203 


Electricity,  168. 

Elements,  of  complexes,  the  results 
of  analysis,  5  et  seq.;  ABC..., 
K L  M .  .  .  ,  a^  v  .  .  ,  ,  8-25,  153;  of 
the  world,  18,  25,  151,  192.  195-196; 
may  be  viewed  as  merely  depend- 
ent on  one  another,  i8i. 

End-organs,  auditive,  123,  127  et  seq., 
142  et  seq.,  147. 

Energy,  174,  175  footnote. 

Entities,  23. 

Environment  and  sensations,  re- 
actions of,  184  footnote. 

Equations,  their  real  and  theoretical 
value,  180. 

Equilibrium,  sense  of,  74  footnote. 

Euclid,  80,  177  footnote. 

Euler,  126,  141,  149. 

Evolution,  applied  to  sense-organs, 
36  footnote;    theory  of,  148. 

Exner,  S.,  70,  125  footnote. 

Experience,  177,  178. 

Explosions,  114,  124,  125  footnote. 

Eyes,  voluntary  and  involuntary 
movements  of,  58-73;  compensa- 
tory movements  of,  in  rotation,  63, 
67.  71. 

Facts,  description  of,  154;  extension 
and  enrichment  of,  by  concepts, 
164 ;  the  goal  of  mental  adaptation, 
165. 

Faraday,  185. 

Fatigue,  of  consciousness,  112;  hy- 
pothesis of  a  material  of,  114  foot- 
note ;  in  hearing,  i34-i35. 

Faust,  38  footnote. 

Fear,  38  footnote. 

Fechner,  39  footnote,  112  footnote, 
121  footnote,  138  footnote. 

Feeling,  12  et  seq.;  and  motion,  191 
et  seq. 

Fidelio,  overture  to,  137. 

Fittest  forms  of  thought,  24. 

Fixation  of  tones,  131-135. 

Flat  as  possible  surfaces,  loi  foot- 
note. 

Force,  defined,  170;  Mayer's  concept 
of,  174- 

Fraunhofer's  lines,  7,  33  footnote. 

Functions,  organic,  38-40. 


Gay-Lussac's  law,  152. 
Geissler's  tube,  113. 
General  images,  160. 
Generalisation,  principle  of  broadest 

possible,  158  et  seq. 
Genius,  149-150. 
Geometry,  space-sensations  and,  45; 

whence  derived,  55-56;  origin  of  its 

cogency,  178. 
Germ-plasm,  39  footnote. 
Ghosts,  fear  of,  37  footnote. 
Goethe,  i. 
Goltz,  37  footnote. 
Graber,  V.,  142  footnote. 
Gravitation,  184  footnote. 
Greeks,  The,  56. 
Groth,  35  footnote. 
Guebhard,  98  footnote. 
Guye,  Dr.,  73  footnote. 

Hallucinations,  87. 

Hankel,  H.,  56. 

Harmonic  musical  combinations, 137. 

Harmonics.     See  Overtones. 

Harmony,  its  explanation,  125  et  seq., 
not  determined  by  beats  alone,  138. 

Hauptmann,  21  footnote,  126. 

Heat,  sensation  of,  180. 

Heidenhain,  51. 

Helmholtz,  32,  120,  122-125,  129  foot- 
note, 139,  141,  147. 

Hensen,  V.,  142  footnote. 

Heptagon,  example  of,  162. 

Heredity,  36  footnote. 

Hering,  23  footnote,  34,  35  footnote, 
36  footnote,  39  footnote,  48  footnote, 
57  footnote,  68,  79  footnote,  80,  81, 
129  footnote. 

Herodotus,  161  footnote. 

Hertz,  186. 

Hindus,  The,  56. 

Holtz.  61. 

Horizontal  symmetry,  50. 

Human  body,  its  relation  to  its  envi- 
ronment, 15  et  seq. 

Huygens,  185,  186. 

Identity,  of  bodies,  9  et  seq.;  per- 
sonal, 20-21  footnote  ;  physiologi- 
cal, 46. 

Illumination,  varying,  r61e  of,  in  rec- 


204 


THE  ANALYSIS  OF  THE  SENSATIONS. 


ognising  objects,  39  footnote;  dif- 
ferences of,  90,  92. 

Illusions  of  sense,  g  footnote. 

Illusive  problems,  13. 

Images,  161. 

Imagination,  influence  of,  on  the  vis- 
ual process,  99. 

Immortality,  4  footnote,  SO  footnote. 

Impact,  184  footnote. 

Indian  geometry,  56. 

Individual,  State  and,  40  footnote. 

Individuality,  4  footnote. 

Innervation,  63,  72,  76  et  seq.;  sensa- 
tions of,  60,  65  et  seq.,  79. 

Insane  persons,  89. 

Instinctive  notions,  12. 

Intellect  and  sensation,  45,  82-84. 

Intelligence,  abnormal,  148-149. 

Intervals,  musical,  characteristic 
sensation  of,  125  et  seq.;  recogni- 
tion of,  136  et  seq.,  147. 

Intuition,  pure,  177. 

Intuitive  knowledge,  157  et  seq. 

Inversion  of  perspective  drawings, 
na. 

Inverted,  objects,  51-52;  vision,  187 
et  seq. 

Investigator,  the,  a  fragment  of  na- 
ture, 165. 

lonians,  161  footnote. 

Italians,  ancient,  106. 

//  thinks,  22. 

James,  Prof.  W.,  73  footnote,  151  foot- 
note. 

Jerking  motion  of  eyes  in  involun- 
tary movement,  62  et  seq.,  72-73. 

Jones,  Owen,  54. 

Judgment,  156  et  seq. 

Kant,  23  footnote,  165. 

Kepler,  172. 

KLM. .  .,  the  complexes.  See  Ele- 
ments. 

Knowledge  of  nature,  what  consti- 
tutes, 151-156. 

Krause,  E.,  42  footnote. 

Kreidl,  78  footnote. 

Kulke,  E.,  136. 

Language,  131  footnote. 

Larynx,  supposed  function  of,  in  the 


formation  of  the  tonal  series,  131 

footnote. 

Law,  definition  of,  156. 

Laws,  170. 

Letters  of  the  alphabet,  confounding 
of,  by  children,  50,  52 ;  their  sym- 
metry, 54-55. 

Lever,  example  of,  x6o,  163. 

Lichtenberg,  22. 

Light-sensations,  deviations  of,  97- 
98 ;  their  relation  with  space-sensa- 
tions predetermined,  188. 

Light-vibrations,  new  chemical  con- 
ception of,  43. 

Lissajous,  105. 

Locke,  65  footnote,  157. 

Locomotion,  44. 

Loeb,  J.,  83  footnote,  200. 

Loewy,  Dr.  Th.,  65  footnote. 

Logarithmic  law  of  Fechner,  39  foot- 
note. 

Lubbock,  Sir  John,  74  footnote,  83 
footnote. 

Ludwig,  Heinrich,  34  footnote. 

Mach,  origin  of  his  philosophical 
and  psychological  views,  182-196. 

Magnet,  170. 

Magnus,  H.,  42  footnote. 

Man,  a  fragment  of  nature,  173. 

Marchfeld,  peasants  of,  42  footnote. 

Marcomanni,  161  footnote. 

Mariotte,  152,  189. 

Marty,  A.,  42  footnote. 

Materialism,  12. 

Mathematics,  its  authority,  17a;  ori- 
gin of  its  cogency,  178. 

Matter,  4,  152. 

Mayer,  Alfred,  33. 

Mayer,  J.  R.,  174-175. 

Mean  of  sensations,  departure  from, 
96  et  seq.,  loi. 

Mechanical,  explanations,40, 184  foot 
note,  193;  ideas,  their  authority, 
172. 

Melody,  136. 

Memory,  organic,  36  footnote;  in 
harmony,  125-126,  148 ;  in  discov- 
ery, 158,  177. 

Mental,  additions  to  facts,  13,  184, 
194;  adaptation,  24,  165,  166,  et  seq. 


INDEX, 


205 


Method,  in  physics  and  psychology, 
I  et  seq.,  13  footnote. 

Mill,  173  footnote. 

Mirror-writing,  132  footnote. 

Molecular  physics,  23  footnote. 

Molecules,  152-154. 

Molifere,  26  footnote. 

Moment,  mechanical,  160. 

Monadic  theories,  15,  183,  184  foot- 
note. 

Monadology,  23  footnote. 

Monism,  12. 

Monistic  conception,  183. 

Monkeys,  music  derived  from  ama- 
tory cries  of,  120. 

Monocular,  vision,  99  et  seq.;  inver- 
sion, 102. 

Morgan,  C.  Lloyd,  39  footnote,  83 
footnote. 

Moths,  82  footnote. 

Motion,  reducing  of  everything  to, 
184  footnote,  193. 

Motor  sensations,  62-79,  ^31  footnote. 

Muller,  Johannes,  i,  29,  86,  87. 

Multiple  response  of  Corti's  organ, 
147. 

Music,  120,  131  footnote,  148-150. 

Myths,  38  footnote. 

Names,  41,  161. 

Naming,  3,  5. 

Nature,  its  unity,  174;  viewed  as  hav- 
ing two  sides,  183. 

Newton,  32,  33,  56,  i72i  185. 

Noises,  122-125,  147. 

Noses,  137. 

Notions.     See  Concepts. 

Nucleus  of  bodies,  metaphysical,  7, 
10,  12,  154,  167. 

Numbers,  sensuous  marks,  determin- 
ing mental  reactions,  162-164,  179, 
180;  theory  of,  dependent  on  expe- 
rience, 178. 

Obtuse  angles,  vision  of,  103-105. 

Oettingen,  A.  von,  125-127,  148. 

Oilcloth,  moving,  experiment  of,  69. 

Oken,  184  footnote. 

One-eyed  people,  81  footnote. 

Optical  space,  80. 

Orator,  ego  of,  11  footnote. 


Organ  for  motor  sensation,  74  et  seq. 
Orientation,  sense  of,  64. 
Other  minds  than  ours,  12  et  seq.,  193. 
Outside  and  inside,  14,  151,  189. 
Overtones,  123, 125, 126, 139, 144  et  seq., 
199. 

Painting,  34  footnote. 

Parallactic  displacements,  in  vision, 
64. 

Parallelism,  of  the  psychical  and 
physical,  30  et  seq.,  80;  of  innerva- 
tion and  sensation,  79. 

Past,  regarded  as  present,  169. 

Patriotism,  19  footnote. 

Pedagogue,  story  of,  4  footnote. 

Percepts,  162. 

Periodic,  motion,  141,  142;  changes, 
175  footnote. 

Permanency,  relative,  of  bodies  and 
the  ego,  3,  4,  et  seq. 

Perpctmun  mobile,  40. 

Personal  equation  of  astronomers, 
61,  112. 

Personality,  its  origin,  character,  and 
import,  18-22. 

Perspective,  monocular,  96-108;  lin- 
ear, 100;  elements  of,  loi ;  inver- 
sion of,  102;  foreshortenings  due 
to,  106. 

Pfaundler,  125  footnote. 

Phantasms,  85-89. 

Philosopher,  the  scourged,  26  foot- 
note. 

Phonic,  126. 

Phylogeny,  as  explanation,  120-121. 

Physharmonica,  133. 

Physical  and  psychical,  no  duality 
between,  195. 

Physical  science,  its  character  and 
influence  on  the  other  sciences, 
1-2;  distinguished  from  physiolo- 
gical and  psychical  science,  194- 
195  ;  its  gain  from  the  analysis  of 
the  sensations,  151  etseq.;  its  func- 
tion, 176;  psychology  and  its  for- 
mer estrangement  from,  182. 

Physiological  and  geometrical  prop- 
erties distinguished,  55. 

Physiology,  influenced  by  physics, 
1-2 ;  defined,  192  et  seq. 


2o6 


THE  ANALYSIS  OF  THE  SENSATIONS. 


Pigeons,  brainless,  37  footnote. 

Pigments,  34  footnote. 

Plane,  the  geometrical,  55,  97. 

Plant-memory,  36  footnote. 

Plateau-Oppel  phenomenon,  70. 

Plateau,  wire-net,  65 ;  film,  102  foot- 
note. 

Pleasure  and  pain,  18. 

Politician,  ego  of,  11  footnote. 

Polle,  Prof.  F.,  42  footnote. 

Polychromy,  42  footnote. 

Pompeiians,  art  of,  42  footnote,  106. 

Popper,  J.,  17  footnote,  23  footnote, 
175  footnote. 

Positive,  factor  in  the  explanation  of 
harmony,  125  et  seq. ;  characteristic 
of  intervals,  148. 

Potential  function,  and  light-sensa- 
tion, 98  footnote ;  loi  footnote. 

Prejudice,  19  footnote. 

Pressure,  184  footnote. 

Preyer,  W.,  24  footnote. 

Probability,  principle  of,  94,  96,  100, 
104. 

Problems,  origin  of,  24 ;  nature  of, 
159  et  seq.,  188, 

Projectile,  example  of,  176. 

Projection,  theory  of,  188. 

Properties,  7,  9. 

Pseudo-problems,  196. 

Psychical  processes,  not  explained 
by  atoms,  153. 

Psychological   analysis,  34   footnote. 

Psychology  of  the  senses,  152-153. 

Psycho-physical  law  of  Fechner,  39 
footnote. 

Pulley,  example  of,  160. 

Purkinje's  after-image,  113. 

Putty,  experiment  with  lumps  of,  59. 

Puzzle-pictures,  93. 

Qualities  of  sensation,  79. 
Quantity,  of  heat  and  electricity,  175 
footnote. 


Railway  trains,  relative  motion  of,  68 

footnote. 
Rates  of  vibration  in  audition,  127  et 

seq.,  140. 
Rays  of  light,  186. 


Reaction-activity,  concepts  a,  163. 

Reactions,  inward  and  outward,  173- 
174.  176. 

Realism,  of  the  average  man,  26. 

Recognition  of  space-figures,  45  et 
seq. 

Reflected  writing,  50-51. 

Reflex  actions  of  animals,  36  foot- 
note. 

Refraction,  28,  33,  159,  187. 

Regularity,  54. 

Relative  motion,  experiments  in,  69. 

Relief,  99  et  seq. 

Religion,  38  footnote. 

Remembrance,  in  harmony,  125-126. 

Repetition,  of  space-figures,  53-55;  a 
principle  in  aesthetics,  53-56. 

Representation,  17,  154 ;  and  sensa- 
tion, 84-85;  organ  of,  85  et  seq.;  of 
facts  in  thought,  153. 

Reproduction,  mental,  156 ;  of  facts 
by  thoughts,  176. 

Research,  aim  of  special,  196. 

Retina,  connexion  of  space-sensa- 
tions with,  57  et  seq. 

Reversible  processes,  115,  175  foot- 
note, i8r. 

Rhythms,  identical,  recognised,  117; 
have  no  symmetry,  115. 

Ribot,  4. 

Riehl,  24  footnote. 

Right  and  left,  confounded,  50-51. 

Right  angles,  vision  of,  103. 

Robert,  W.,  115  footnote. 

Rollett,  37  footnote. 

Romans,  161  footnote. 

Rotation,  sensation  of,  66-68;  of  ani- 
mals, experiments  on,  74-76  foot- 
note. 

Saliency,  optical,  98. 

Sameness,  9  et  seq. 

Santonine,  13. 

Saunderson,  65  footnote. 

Scaffolding,  artificial,  in  science,i83. 

Schneider,  38. 

Scholar,  his  struggle  for  existence, 

19  footnote. 
Schopenhauer,  1,  119,  120  footnote. 
Schuster,  36  footnote. 
Science,  aim  of,  18,  22,  153,  156. 


INDEX. 


J07 


Scientist,  his  struggle  for  existence, 
19  footnote. 

Sectors,  experiment  with  black  and 
white,  97-98. 

Seebeck,  A.,  141. 

Seeliger,  200. 

Semi-circular  canals,  their  function 
in  orientation,  74  footnote. 

Sensation,  and  thing,  11;  modes  of 
analysing,  29  et  seq.;  interchange- 
able qualities  of,-92 ;  of  time,  a  new 
specific  energy,  116;  and  under- 
standing, distinguished,  140. 

Sensations,  2,  7,  10,  12  et  seq.,  14,  18; 
elements  of  the  world,  25;  of  move- 
ment, 62-79;  representations,  and 
intellect,  relations  between,  82-84; 
lie  at  the  basis  of  all  the  physicist's 
work,  191  et  seq.;  attributing  of,  to 
animals  and  other  people,  21  foot- 
note, 193. 

Sense,  illusions  of,  9  footnote  ;  mem- 
ory of,  87;  world  of,  151. 

Senses,  the  investigation  of  the,  29  et 
seq.,  160,  164. 

Sense-organs,  their  origin,  evolution, 
and  functions,  36-40;  have  their 
own  independent  life,  memory,  and 
intelligence,  86-89. 

Shading  of  bodies,  90  et  seq. 

Sight.     See  Visual. 

Sight-sensations,  41-42,  82-108;  parts 
of  complexes,  82. 

Sight-space,  80. 

Silk-worm,  adaptive  power  of,  38 
footnote. 

Similar  tonal  constructs,  136. 

Similarity,  geometrical  and  optical, 
46  et  seq. 

Similitude,  principle  of,  in  mechan- 
ics, 56. 

Singing,  131  footnote, 

Skin-sensations,  65-66. 

Sleep,  112. 

Snowfall,  produces  rising  motion  of 
observer,  71  footnote. 

Solid  bodies,  vision  of,  105-108. 

Soret,  J.  L.,  56  footnote. 

Soul,  4  ;  seat  of  the,  21  footnote. 

Sound-sensations,  32. 

Sound-waves,  186. 


Space,  and  time,  7  et  seq.;  conception 
of,  dependent  on  physical  experi- 
ence, 177;  geometrical,  80,  177. 

Space-sensations,  31,  42,  44-82;  pro- 
duced by  the  motor-apparatus  of 
the  eye,  49;  the  information  they 
yield,  49;  defined  as  will,  59-60. 

Sparrow,  young,  37. 

Species,  preservation  of,  40,  120. 

Specific  energies,  85;  115-116;  in 
audition,  127  et  seq.,  140;  two  only 
required  for  the  perception  of 
tones,  143  et  seq.;  theory  of  the 
two,  147;  their  vahie,  193  footnote. 

Specific  inductive  capacity,  185. 

Spectrum,  28-29,  32,  155. 

Spencer,  36  footnote,  38  footnote. 

Sphere,  97. 

Spiritualism,  philosophical,  12. 

Square  numbers,  162. 

State,  the  individual  and,  40  foot- 
note. 

Stereoscopic  effects,  97. 

Straight  lines,  symmetry  of,  52-53. 55; 
properties  of,  95,  96. 

Strauss,  David,  38  footnote. 

Strieker,  131  footnote,  173  footnote. 

Stumpf,  119  footnote,  143. 

Substance,  166  et  seq. 

Sucking  of  youag  animals,  37  foot- 
note. 

Superstition,  37  footnote. 

Supplementary  colorings,  acoustic, 
144  et  seq.,  147. 

Supplementing.     See  Completing, 

Surfaces,  flat,  loi  footnote. 

Surgeon,  optical  illusion  of,  112. 

Symbols,  economical,  152  et  seq. 

Symmetrical  movements,  51. 

Symmetry,  46;  vertical,  51;  lacking 
in  rhythm,  115;  in  music,  126  foot- 
note. 

Talent,  149-150. 
Tannhauser,  overture  to,  136. 
Teleology,  in  research,  36-40,  80. 
Temperature,  excess   of,  substituted 

for  time,  180-181. 
Terminal  organ  of  acceleration,  74. 
Theories,   mere    helps   to  facilitate 

thought,  187. 


2o8 


THE  ANALYSIS  OF  THE  SENSATIONS, 


Theory  of  colors,  44 ;  nature  of,  185 
et  seq. 

Thermometers,  180. 

Thing,  151.     See  Bodies. 

Thing-in-itself,  6  et  seq. 

Thought,  by  concepts,  a  reaction- 
activity,  164. 

Thoughts,  familiar,  165;  weak,  sup- 
ported by  strong,  172. 

Timbre,  130,  134. 

Time,  and  space,  7  et  seq.;  sensation 
of,  109-118,  179;  irreversibility  of, 
115;  perspective  contraction  of, 
117 ;  passage  of,  169 ;  physical,  179 ; 
may  be  eliminated  from  events, 
180;  not  reversible,  181. 

Tone-sensations,  119  et  seq.;  function 
of,  in  the  preservation  of  life,  122 ; 
common  factors  of,  128 ;  an  analysis 
of,  127  et  seq.;  compared  with  color- 
sensations,  130;  space-analogue  of, 
130,  131 ;  optical  analogue  of,  135 ; 
requirements  of  a  more  complete 
theory  of,  141  et  seq.;  Mach's  new 
hypothetical  analysis  of,  141-148. 

Tones,  distinguishing  of,  129;  num- 
ber of  vibrations  necessary  for 
producing,  197-199. 

Tonic,  126. 

Touch,  compared  with  hearing,  142 
footnote. 

Transference  of  theories,  from  phys- 
ics to  psychology,  187-195. 

Unconditioned  permanent  things, 
196. 

Unconscious  reasoning,  85. 

Understanding  and  sensation,  dis- 
tinguished, 140. 

Undertones,  144. 

Undulatory  theory  of  light,  185. 

Unity  of  the  soul,  21  footnote;  men- 
tal, 184  footnote. 

Universals,  i6o. 

Urvasi,  132  footnot*. 


Vanishing  points,  100. 

Vertical  lines,  96. 

Vertigo,  optical,  67;   in  deaf-mntes, 

73  footnote. 
Vibrational  rates,  142  et  seq. 
Vibrations,  number  of,  necessary  to 

the  sensation  of  sound,  124,  and 

Appendix  II. 
Vierordt,  70. 
Vinci,  Leonardo  da,  34  footnote,  35 

footnote,  88  footnote,  137. 
Virgil,  42  footnote. 
Virtuoso,  musical  ego  of,  11  footnote. 
Visiting  card,  experiment  of,  91,  102. 
Visual,  pnrple,  43  ;  apparatus,  49-50  ; 

process,  81 ;     sense,   organic    and 

elemental  habitudes  of,  94,  107. 
Voice,  human,  119  et  seq. 

Walls  and  moat  of  a  city,  13  footnote. 

Weber,  39  footnote. 

Weismann,  20  footnote.  36  footnote, 
38  footnote,  39  footnote,  150. 

Whirling  machine  for  observing  the 
conduct  of  animals  in  rotation,  74 
footnote  et  seq. 

Will,  determines  space-sensations, 
59  et  seq.,  68;  is  the  sensation  of 
movement,  72 ;  represented  in  mu- 
sic, 120. 

Witchcraft,  38  footnote. 

Within  and  without,  44,  151,  189. 

Witticisms,  132  footnote. 

Wollaston,  33. 

Words,  nature  of,  131. 

Work,  mechanical,  160,  174,  175  foot- 
note. 

World,  a  mass  of  sensations,  23  foot- 
note. 

World-purpose,  38, 

Writing,  50. 

Young,  Thomas,  33. 
20ilner's  pseudoscopy,  io3« 


THE  WORKS  OF  KUNST  MACH. 

THE   SCIENCE   OF  MECHANICS, 

A  CRITICAL  AND  HISTORICAL  EXPOSITION  OF  ITS 
PRINCIPLES. 

By  DR.  ERNST  MACH. 

PROFESSOR  OF  THE  HISTORY  AND  THEORY  OF  INDUCTIVE  SCIENCE  IN  THE 
UNIVERSITY  OF  VIENNA. 

Translated  from  the  Second  German  Edition 
By  THOMAS  J.  McCORMACK. 


250  Cuts.  534  Pages.  Half  Morocco,  Gilt  Top,  Marginal  Analyses. 
Exhaustive  Index.    Price  $2.50. 


TABLE  OF  CONTENTS. 

Statics. 
The  Lever.  Virtual  Velocities. 

The  Inclined  Plane.  Statics  in  Their  Application  to  Fluids 

The  Composition  of  Forces.  Statics  in  Their  Application  to  Gases. 

Dynamics. 

Galileo' s  Achievements.  Newton' s  Views  of  Time,  Space,  and 

Achievements  of  Huygens.  Motion. 

Achievements  of  Newton.  Critique  of  the  Newtonian  Enuncia- 

Principle  of  Reaction.  tions. 

Criticism  of  the  Principle  of  Reac-  Retrospect  of  the  Development  of 

tion  and  of  the  Concept  of  Mass.  Dynamics. 

The  Extension  of  thk  Principles  of  Mechanics. 

Scope  of  the  Newtonian  Principles.  Principle  of  Vis  Viva. 

Formulae  and  Units  of  Mechanics.  Principle  of  Least  Constraint 

Conservation  of  Momentum,  Conser-  Principle  of  Least  Action. 

vation  of  the  Centre  of  Gravity,  Hamilton' s  Principle. 

and  Conservation  of  Areas.  Hydrostatic  and  Hydrodynamic 
Laws  of  Impact.  Questions. 

D'Alembert's  Principle. 

Formal  Development  of  Mechanics. 
The  Isoperimetrical  Problems.  Analytical  Mechanics. 

Theological,  Animistic,  and  Mystical       The  Economy  of  Science. 
Points  of  View  in  Mechanics. 

The  Relation  of  Mechanics  to  Other  Departments  of  Knowledge. 
Relations  of  Mechanics  to  Physics.  Relations  of  Mechanics  to  Physiology 


THE  WORKS  OF  ERNST  MACH. 

PRESS  NOTICES. 

"The  appearance  of  a  translation  into  English  of  this  remarkable  book 
should  serve  to  revivify  in  this  country  [England]  the  somewhat  stagnating 
treatment  of  its  subject,  and  should  call  up  the  thoughts  which  puzzle  us  when 
we  think  of  them,  and  that  is  not  sufficiently  often.  .  .  .  Professor  Mach  is  a 
striking  instance  of  the  combination  of  great  mathematical  knowledge  with 
experimental  skill,  as  exemplified  not  only  by  the  elegant  illustrations  of  me- 
chanical principles  which  abound  in  this  treatise,  but  also  from  his  brilliant 
experiments  on  the  photography  of  bullets.  ...  A  careful  study  of  Professor 
Mach's  work,  and  a  treatment  with  more  experimental  illustration,  on  the 
lines  laid  down  in  the  interesting  diagrams  of  his  Science  of  Mechanics,  will 
do  much  to  revivify  theoretical  mechanical  science,  as  developed  from  the 
elements  by  rigorous  logical  treatment,"— Prof.  A.  G.  Greenhill,  in  Nature, 
London. 

"Those  who  are  curious  to  learn  how  the  principles  of  mechanics  have 
been  evolved,  from  what  source  they  take  their  origin,  and  how  far  they  can 
be  deemed  of  positive  and  permanent  value,  will  find  Dr.  Mach's  able  trea- 
tise entrancingly  interesting.  .  .  .  The  book  is  a  remarkable  one  in  many  re- 
spects, while  the  mixture  of  history  with  the  latest  scientific  principles  and 
absolute  mathematical  deductions  makes  it  exceedingly  attractive." — Me- 
chanical World,  Manchester  and  London,  England. 

"  Mach's  Mechanics  is  unique.  It  is  not  a  text-book,  but  forms  a  useful 
supplement  to  the  ordinary  text-book.  The  latter  is  usually  a  skeleton  out- 
line, full  of  mathematical  symbols  and  other  abstractions.  Mach's  book  has 
•muscle  and  clothing,'  and  being  written  from  the  historical  standpoint,  in- 
troduces the  leading  contributors  in  succession,  tells  what  they  did  and  how 
they  did  it,  and  often  what  manner  of  men  they  were.  Thus  it  is  that  the 
pages  glow,  as  it  were,  with  a  certain  humanism,  quite  delightful  in  a  scien- 
tific book.  .  .  .  The  book  is  handsomely  printed,  and  deserves  a  warm  recep- 
tion from  all  interested  in  the  progress  of  science.''— The  Physical  Review,  New 
York  and  London. 

"  Mr.  T.  J.  McCormack,  by  his  effective  translation,  where  translation 
was  no  light  task,  of  this  masterly  treatise  upon  the  earliest  and  most  funda- 
mental of  the  sciences,  has  rendered  no  slight  service  to  the  English  speak- 
ing student.  The  German  and  English  languages  are  generally  accounted 
second  to  none  in  their  value  as  instruments  for  the  expression  of  scientific 
thought;  but  the  conversion  bodily  of  an  abstruse  work  from  one  into  the 
other,  so  as  to  preserve  all  the  meaning  and  spirit  of  the  original  and  to  set  it 
easily  and  naturally  into  its  new  form,  is  a  task  of  the  greatest  difficulty,  and 


THE  WORKS  or  ERNST  MACH. 

when  performed  so  well  as  in  the  present  instance,  merits  great  commenda- 
tion. Dr.  Mach  has  created  for  his  own  works  the  severest  possible  standard 
of  judgment.  To  expect  no  more  from  the  books  of  such  a  master  than  from 
the  elementary  productions  of  an  ordinary  teacher  in  the  science  would  be 
undue  moderation.  Our  author  has  lifted  what,  to  many  of  us,  was  at  one 
time  a  course  of  seemingly  unprofitable  mental  gymnastics,  encompassed 
only  at  vast  expenditure  of  intellectual  effort,  into  a  study  possessing  a  deep 
philosophical  value  and  instinct  with  life  and  interest.  *No  profit  grows 
where  is  no  pleasure  ta'en,'  and  the  emancipated  collegian  will  turn  with 
pleasure  from  the  narrow  methods  of  the  text-book  to  where  the  science  is 
made  to  illustrate,  by  a  treatment  at  once  broad  and  deep,  the  fundamental 
connexion  between  all  the  physical  sciences,  taken  together." — The  Mining 
Journal,  London,  England. 

"As  a  history  of  mechanics,  the  work  is  admirable." — The  Nation,  New 
York. 

"An  excellent  book,  admirably  illustrated."— 7%^  ZzV^rary  World,  Lon- 
don, England. 

"Sets  forth  the  elements  of  its  subject  with  a  lucidity,  clearness,  and 
force  unknown  in  the  mathematical  text-books  ....  is  admirably  fitted  to 
serve  students  as  an  introduction  on  historical  lines  to  the  principles  of  me- 
chanical science." — Canadian  Mining  and  Mechanical  Review,  Ottawa,  Can. 

"A  masterly  book.  ...  To  any  one  who  feels  that  he  does  not  know  as 
much  as  he  ought  to  about  physics,  we  can  commend  it  most  heartily  as  a 
scholarly  and  able  treatise  ....  both  interesting  and  profitable." — ^A.  M. 
Wellington,  in  Engineering  News,  New  York. 

"The  book  as  a  whole  is  unique,  and  is  a  valuable  addition  to  any  library 
of  science  or  philosophy.  .  .  .  Reproductions  of  quaint  old  portraits  and 
vignettes  give  piquancy  to  the  pages.  The  numerous  marginal  titles  form  a 
complete  epitome  of  the  work ;  and  there  is  that  invaluable  adjunct,  a  good 
index.  Altogether  the  publishers  are  to  be  congratulated  upon  producing  a 
technical  work  that  is  thoroughly  attractive  in  its  make-up."— Prof.  D.  W. 
Hering,  in  Science. 

"There  is  one  other  point  upon  which  this  volume  should  be  commended, 
and  that  is  the  perfection  of  the  translation.  It  is  a  common  fault  that  books 
of  the  greatest  interest  and  value  in  the  original  are  oftenest  butchered  or 
made  ridiculous  by  a  clumsy  translator.  The  present  is  a  noteworthy  excep- 
tion."— Railway  Age. 


THE  WORKS  OF  ERNST  MACH. 

"The  book  is  admirably  printed  and  bound.  .  .  .  The  presswork  is  nn- 
excelled  by  any  technical  books  that  have  come  to  our  hands  for  some  time, 
and  the  engravings  and  figures  are  all  clearly  and  well  executed," — Railroad 
GoMttt*. 

TESTIMONIALS  OF  PROMINENT  EDUCATORS. 

"  I  am  delighted  with  Professor  Mach's  Science  of  Mechanics."— M.  E. 
CooUy,  Professor  of  Mechanical  Engineering,  Ann  Arbor,  Mich. 

"You  have  done  a  good  service  to  science  in  publishing  Mach's  Science 
of  Mechanics  in  English.  I  shall  take  every  opportunity  to  recommend  it  to 
young  students  as  a  source  of  much  interesting  information  and  inspiration." 
—M.  I.  Pupin,  Professor  of  Mechanics,  Columbia  College,  New  York. 

"Mach's  Science  of  Mechanics  is  an  admirable  ....  book."— /Vi?/^  E.  A. 
Fuertes,  Director  of  the  College  of  Civil  Engineering  of  Cornell  University, 
Ithaca.  N.  Y. 

"I  congratulate  you  upon  producing  the  work  in  such  good  style  and  in 
so  good  a  translation.  I  bought  a  copy  of  it  a  year  ago,  very  shortly  after  you 
issued  it.  The  book  itself  is  deserving  of  the  highest  admiration;  and  you 
are  entitled  to  the  thanks  of  all  English-speaking  physicists  for  the  publica- 
tion of  this  translation."— Z>.  W./T-rr/w^,  Professor  of  Physics,  University  of 
th«  City  of  New  York,  New  York. 

"  I  have  read  Mach's  Science  of  Mechanics  with  great  pleasure.  The  book 
is  exceedingly  interesting."— fT.  i'".  i»/a^V,  Professor  of  Physics,  Princeton 
University,  Princeton,  N.  J. 

"Tha  Science  of  Mechanic*  by  Mach,  translated  by  T.  J.  McCormack,  I 
regard  as  a  most  valuable  work,  not  only  for  acquainting  the  student  with  the 
history  of  the  development  of  Mechanics,  but  as  serving  to  present  to  him 
most  favorably  the  fundamental  ideas  of  Mechanics  and  their  rational  con- 
nexion with  the  highest  mathematical  developments.  It  is  a  most  profitable 
book  to  read  along  with  the  study  of  a  text-book  of  Mechanics,  and  I  shall 
take  pleasure  in  recommending  its  perusal  by  my  students.'  '—S.  W.  Robinson, 
Professor  of  Mechanical  Engineering,  Ohio  State  University,  Columbus,  Ohio. 

"  I  am  de^ghted  with  Mach's  '  Mechanics.'  I  will  call  the  attention  to 
it  of  students  and  instructors  who  have  the  Mechanics  or  Physics  to  study  or 
teach."—/.  E.  Davies,  University  of  Wisconsin,  Madison,  Wis. 

"There  can  be  but  one  opinion  as  to  the  value  of  Mach's  work  in  this 
translation.  No  instructor  in  physics  should  be  without  a  copy  of  it."— Henry 
Crew,  Professor  of  Physics  in  the  Northwestern  University,  Evanston.  III. 


THE  WORKS  OF  ERNST  MACH. 

POPULAR  SCIENTIFIC  LECTURES. 

A  PORTRAYAL  OF  THE  SPIRIT  AND  METHODS 
OF  SCIENCE. 

By  DR.  ERNST  MACH. 

PROFESSOR  OF  THE  HISTORY  AND  THEORY  OF  INDUCTIVE  SCIENCE  IN  THE 

UNIVERSITY  OF  VIENNA. 

Translated  by  THOMAS  J.  McCORMACK. 


Cloth,  Gilt  Top.     Exhaustively  Indexed,     Pages,  313.    Cuts,  44.    Price,  $1.00. 


TITLES  OF  THE  LECTURES. 

The  Forms  of  Liquids.  On  the  Economical  Nature  of  Phys- 

The  Fibres  of  Corti.  ical  Inquiry. 

On  the  Causes  of  Harmony.  On  Transformation  and  Adaptation 

On  the  Velocity  of  Light.  in  Scientific  Thought. 

Why  has  Man  Two  Eyes?  On  the  Principle  of  Comparison  in 

On  Symmetry.  Physics. 

On   the    Fundamental    Concepts  of        On  the  Relative  Educational  Value 

Static  Electricity.  of  the  Classics  and  the  Mathemat- 

On  the  Principle  of  the  Conservation  ico-Physical  Sciences. 

of  Energy. 

PRESS  NOTICES. 

"A  most  fascinating  volume,  treating  of  phenomena  in  which  all  are  in- 
terested, in  a  delightful  style  and  with  wonderful  clearness.  For  lightness 
of  touch  and  yet  solid  value  of  information  the  chapter  '  Why  Has  Man  Two 
Eyes? '  has  scarcely  a  rival  in  the  whole  realm  of  popular  scientific  writing." 
—The  Boston  Traveller. 

"Truly  remarkable  in  the  insight  they  give  into  the  relationship  of  the 
various  fields  cultivated  under  the  name  of  Physics.  ...  A  vein  of  humor  is 
met  here  and  there  reminding  the  reader  of  Heaviside,  never  offending  one's 
taste.  These  features,  together  with  the  lightness  of  touch  with  which  Mr. 
McCormack  has  rendered  them,  make  the  volume  one  that  may  be  fairly 
called  rare.  The  spirit  of  the  author  is  preserved  in  such  attractive,  really 
delightful,  English  that  one  is  assured  nothing  has  been  lost  by  translation." 
—Prof.  Henry  Crew,  in  The  Astrophysical  Journal. 


THE  WORKS  OF  ERNST  MACH. 

"A  very  delightful  and  useful  book.  .  .  .  The  author  treats  some  of  the 
most  recondite  problems  of  natural  science,  in  so  charmingly  untechnical  a 
way,  with  such  a  wealth  of  bright  illustration,  as  makes  his  meaning  clear  to 
the  person  of  ordinary  intelligence  and  education.  .  .  .  This  is  a  work  that 
should  find  a  place  in  every  library,  and  that  people  should  be  encouraged  to 
read." — Daily  Picayune,  New  Orleans. 

"  In  his  translation  Mr.  McCormack  has  well  preserved  the  frank,  sim- 
ple, and  pleasing  style  of  this  famous  lecturer  on  scientific  topics.  Professor 
Mach  deals  with  the  live  facts,  the  salient  points  of  science,  and  not  with  its 
mysticism  or  dead  traditions.  He  uses  the  simplest  of  illustrations  and  ex- 
presses himself  clearly,  tersely,  and  with  a  delightful  freshness  that  makes 
entertaining  reading  of  what  in  other  hands  would  be  dull  and  prosy." — En- 
gineering News,  N.  Y. 

•*  The  general  reader  is  led  by  plain  and  easy  steps  along  a  delightful  way 
through  what  would  be  to  him  without  such  a  help  a  complicated  maze  of 
difficulties.  Marvels  are  invented  and  science  is  revealed  as  the  natural  foe 
to  mysteries." — The  Chautauguan, 

•'The  beautiful  quality  of  the  work  is  not  marred  by  abstruse  discussions 
which  would  require  a  scientist  to  fathom,  but  is  so  simple  and  so  clear  that 
it  brings  us  into  direct  contact  with  the  matter  treated." — The  Boston  Post. 

••A  masterly  exposition  of  important  scientific  truths." — Scotsman,  Edin- 
burgh. 

"  These  lectures  by  Dr.  Mach  are  delightfully  simple  and  frank  ;  there  is 
no  dryness  or  darkness  of  technicalities,  and  science  and  common  life  do  not 
seem  separated  by  a  gulf.  . . .  The  style  is  admirable,  and  the  whole  volume 
seems  gloriously  alive  and  human." — Providence  Journal,  R.  I. 

"  The  non-scientific  reader  who  desires  to  learn  something  of  modern 
scientific  theories,  and  the  reasons  for  their  existence,  cannot  do  better  than 
carefully  study  these  lectures.  The  English  is  excellent  throughout,  and  re- 
flects great  credit  on  the  iransls^toT.**— Manufacturer  and  Builder. 

••We  like  the  quiet,  considerate  intelligence  of  these  lectures." — Inde- 
pendent, New  York. 

"  Professor  Mach's  lectures  are  so  pleasantly  written  and  illumined  with 
such  charm  of  illustration  that  they  have  all  the  interest  of  lively  fiction."— 
New  York  Com.  Advertiser. 

••The  literary  and  philosophical  suggestiveness  of  the  book  is  very  rich." 
Hartford  Seminary  Record. 


THE  WORKS  OF  ERNST  MACH. 

"All  are  presented  so  skilfully  that  one  can  imagine  that  Professor  Mach's 
hearers  departed  from  his  lecture-room  with  the  conviction  that  science  was 
a  matter  for  abecedarians.  Will  please  those  who  find  the  fairy  tales  of  sci- 
ence more  absorbing  than  fiction." — The  Pilot,  Boston. 

"Professor  Mach  ...  is  a  master  in  physics.  .  .  .  His  book  is  a  good  one 
and  will  serve  a  good  purpose,  both  for  instruction  and  suggestion."— Prof. 
A.  E.  Dolbear,  in  The  Dial. 

"The  most  beautiful  ideas  are  unfolded  in  the  exposition."— Cazf/z^^/zV 
World,  New  York. 


"A  wonderfully  original  little  book."— /V*?/".  \V.  Jatncs,  of  Harvard. 

Contributions  to  the  Analysis  of  the 
Sensations. 

By  DR.  ERNST  MACH. 

PROFESSOR  OF  THE  HISTORY  AND  THEORY  OF  INDUCTIVE  SCIENCi:  IN  THE 
UNIVERSITY  OF  VIENNA. 


Pages,  208.     Illustrations,  37.     Indexed 
Price,  Cloth,  $1.25. 


CONTENTS, 

Introductory:  Antimetaphysiral.  The  Sensation  of  Time. 

The  Chief  Points  of  View  for  the  In-  The  Sensation  of  Sound. 

vustij^ation  of  the  Senst^s.  Infliuence  of  the  Preceding  Investiga- 

The  Space-Sensations  of  tlie  Eye.  tions  on  the  Mode  of  Conceiving 

Space-Sensations,  Cotitiniied  Physics. 

The   Relations  of    the   Sight-Sensa-  Facts  and  Mental  Symbols. 

tions  to  One  Another  and  to  the  A  New  Acoustic  Experiment. 

Other  Psychical  Elements. 


CHICAGO: 

THE  OPEN  COURT  PUBLISHING  CO., 

324  DEARBORN  STREET, 
LONDON  ADDRESS:  17  Johnson's  Court,  Fleet  St.,  E.  C. 


THE  OPEN   COURT 

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THE  MONIST 

A  QUARTERLY  MAGAZINE  OF 

PHILOSOPHY  AND  SCIENCE. 


THE  MONIST  discusses  the  fundamental  problems  of  Philosophy  in 
their  practical  relations  to  the  religious,  ethical,  and  sociological  questions 
of  the  day.    The  following  have  contributed  to  its  columns  : 

Prof.  Joseph  Le  Conte,  Prof.  G.  J.  Romanes,  Prof.  C.  Lombroso, 

Dr.  W:  T.  Harris,  Prof.  C.  Lloyd  Morgan,  Prof.  E.  Haeckel 

M.  D.  CoNWAV,  James  Sully,  Prof.  H.  HSffding, 

Charles  S.  Peirce,  B.  Bosanquet,  Dr.  F.  Oswald, 

Prof.  F.  Max  MOller,  Dr.  A.  Binet,  Prof.  J.  Delbceuf, 

Prof.  E.  D.  Cope,  Prof.  Ernst  Mach,  Prof.  F.  Jodl, 

Carus  SterneT,  Rabbi  Emil  Hirsch,  Prof.  H.  M.  Stanley, 

Mrs.  C.  Ladd  Franklin,  Lester  F.  Ward,  G.  Ferrero, 

Prof.  Max  Verworn,  Prof.  H.  Schubert,  J.  Venn, 

Prof.  Felix  Klein,  Dr.  Edm.  Montgomery,  Prof.  H.  von  Holst. 

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THE  PRIMARY  FACTORS  OF  ORGANIC  EVOLUTION. 
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MULLER,  F.   MAX. 

THREE    INTRODUCTORY    LECTURES    ON    THE    SCIENCE    OF 
THOUGHT. 
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ROMANES,  GEORGE  JOHN. 

DARWIN  AND  AFTER  DARWIN. 

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THOUGHTS  ON  RELIGION. 

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THE  PSYCHOLOGY  OF  ATTENTION. 
THE  DISEASES  OF  PERSONALITY. 
THE  DISEASES  OF  THE  WILL. 

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THE  SCIENCE  OF  MECHANICS. 

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POPULAR  SCIENTIFIC  LECTURES. 

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THE  ANALYSIS  OF  THE  SENSATIONS. 

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GOODWIN.  REV.  T.  A. 

LOVERS  THREE  THOUSAND  YEARS  AGO. 

As  Indicated  by  the  Song  of  Solomon.     Pp.  41.     Boards,  50c. 

HOLYOAKE,  G.  J. 

ENGLISH  SECULARISM.    A  Confession  of  Belief. 
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CORNILL,  CARL  HEINRICH. 
THE  PROPHETS  OF  ISRAEL. 

Popular  Sketches  from  Old  Testament  History.    Pp.,  200.   Cloth,  Ji.oo. 
THE  RISE  OF  THE  PEOPLE  OF  ISRAEL. 
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THE  PSYCHIC  LIFE  OF  MICRO-ORGANISMS. 

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ON  DOUBLE  CONSCIOUSNESS. 

Studies  in  Experimental  Psychology.    93  pages.    Paper,  15  cents. 

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CHRISTIANITY  AND  PATRIOTISM. 
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A  PILGRIMAGE  TO  BEETHOVEN. 

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WEISMANN,  AUGUST. 

GERMINAL  SELECTION.    As  a  Source  of  Definite  Variation. 
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NOIRE,  LUDWIG. 

ON  THE  ORIGIN  OF  LANGUAGE.     Pp.  57-     Paper,  15c. 

FREYTAG,  GUSTAV. 

THE  LOST  MANUSCRIPT.     A  Novel. 

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MARTIN  LUTHER. 

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HERING,  EWALD. 

ON  MEMORY,  and  THE  SPECIFIC  ENERGIES  OF  THE  NERVOUS 
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THE  FREE  TRADE  STRUGGLE  IN  ENGLAND. 

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WHEELBARROW  :  Articles  and  Discussions  on  the  Labor  Question. 

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GOETHE  AND  SCHILLER'S  XENIONS. 

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ANCIENT  INDIA:    ITS  LANGUAGE  AND  RELIGIONS. 
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THE  ETHICAL  PROBLEM. 

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FUNDAMENTAL  PROBLEMS. 

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HOMILIES  OF  SCIENCE. 

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THE  IDEA  OF  GOD. 

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THE  SOUL  OF  MAN. 

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TRUTH  IN  FICTION.     Twelve  Tales  with  a  Moral. 

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THE  RELIGION  OF  SCIENCE. 

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PRIMER  OF  PHILOSOPHY. 

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THE  PHILOSOPHY  OF  THE  TOOL. 

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OUR  NEED  OF  PHILOSOPHY. 

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SCIENCE  A  RELIGIOUS  REVELATION. 

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THE  GOSPEL  OF  BUDDHA.     According  to  Old  Records. 

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THE  REDEMPTION  OF  THE  BRAHMAN.    A  Tale  of  Hindu  Life. 

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THE  PHILOSOPHY  OF  ANCIENT  INDIA. 

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EPITOMES  OF  THREE  SCIENCES. 

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